This paper presents a study on pressure and velocity boundary conditions and bounceback for the lattice Boltzmann BGK model (LBGK). The authors propose a new method to specify these conditions, which are constructed in consistency with the wall boundary condition based on an idea of bounceback of non-equilibrium distribution. When used with the improved incompressible LBGK model, the simulation results recover the analytical solution of the plane Poiseuille flow driven by pressure (density) difference with machine accuracy. The half-way wall bounceback boundary condition is used with pressure (density) inlet/outlet conditions proposed in this paper and in [2] to study the 2-D Poiseuille flow and the 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback is comparable with that using some other published boundary conditions. Additionally, the bounceback condition has a much better stability behavior than that of other boundary conditions. The paper discusses the derivation of pressure or velocity flow boundary conditions for the 2-D square lattice LBGK model. The authors propose a new boundary condition based on an idea of bounceback on the non-equilibrium part. The boundary conditions are applied to the modified incompressible LBGK model (d2q9i) and produce results of machine accuracy for 2-D Poiseuille flow with pressure (density) or velocity inlet/outlet conditions. The paper also discusses the numerical results of the model d2q9i, showing that the velocity field is uniform in the x-direction and accurate up to machine accuracy compared to the analytical solution. The density is uniform in the cross channel direction and linear in the flow direction. The results show that the half-way wall bounceback boundary condition gives second-order accuracy for the 2-D Poiseuille flow and the 3-D square duct flow. The paper also discusses the stability issue related to boundary conditions, finding that the combination of bounceback without collision on stationary walls with equilibrium distribution at flow boundaries gives the best behavior on stability. The half-way wall bounceback is recommended for stationary walls due to its better stability behavior. The paper also discusses the flow boundary conditions and results for the 3-D 15-velocity LBGK model (d3q15) and an incompressible model (d3q15i). The authors perform simulations on the 3-D square duct flow using the pressure flow boundary condition and report the results. The results show that the half-way wall bounceback boundary condition gives an accuracy close to second-order for the 3-D square duct flow. The paper concludes that the half-way wall bounceback boundary condition is recommended for stationary walls due to its better stability behavior and that the flow boundary conditions proposed in this paper or in [2] are suitable for flow boundary conditions in simulations of small to moderate Re numbers.This paper presents a study on pressure and velocity boundary conditions and bounceback for the lattice Boltzmann BGK model (LBGK). The authors propose a new method to specify these conditions, which are constructed in consistency with the wall boundary condition based on an idea of bounceback of non-equilibrium distribution. When used with the improved incompressible LBGK model, the simulation results recover the analytical solution of the plane Poiseuille flow driven by pressure (density) difference with machine accuracy. The half-way wall bounceback boundary condition is used with pressure (density) inlet/outlet conditions proposed in this paper and in [2] to study the 2-D Poiseuille flow and the 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback is comparable with that using some other published boundary conditions. Additionally, the bounceback condition has a much better stability behavior than that of other boundary conditions. The paper discusses the derivation of pressure or velocity flow boundary conditions for the 2-D square lattice LBGK model. The authors propose a new boundary condition based on an idea of bounceback on the non-equilibrium part. The boundary conditions are applied to the modified incompressible LBGK model (d2q9i) and produce results of machine accuracy for 2-D Poiseuille flow with pressure (density) or velocity inlet/outlet conditions. The paper also discusses the numerical results of the model d2q9i, showing that the velocity field is uniform in the x-direction and accurate up to machine accuracy compared to the analytical solution. The density is uniform in the cross channel direction and linear in the flow direction. The results show that the half-way wall bounceback boundary condition gives second-order accuracy for the 2-D Poiseuille flow and the 3-D square duct flow. The paper also discusses the stability issue related to boundary conditions, finding that the combination of bounceback without collision on stationary walls with equilibrium distribution at flow boundaries gives the best behavior on stability. The half-way wall bounceback is recommended for stationary walls due to its better stability behavior. The paper also discusses the flow boundary conditions and results for the 3-D 15-velocity LBGK model (d3q15) and an incompressible model (d3q15i). The authors perform simulations on the 3-D square duct flow using the pressure flow boundary condition and report the results. The results show that the half-way wall bounceback boundary condition gives an accuracy close to second-order for the 3-D square duct flow. The paper concludes that the half-way wall bounceback boundary condition is recommended for stationary walls due to its better stability behavior and that the flow boundary conditions proposed in this paper or in [2] are suitable for flow boundary conditions in simulations of small to moderate Re numbers.