The paper presents a method for solving small-strain plasticity problems using a discrete dislocation model. The dislocations are represented as line defects in a linear elastic medium, and the solution is expressed as the superposition of the infinite-medium solution for the dislocations and a complementary solution that enforces boundary conditions on the finite body. The complementary solution is obtained from a finite-element solution of a linear elastic boundary value problem. The lattice resistance to dislocation motion, dislocation nucleation, and annihilation are incorporated into the formulation through constitutive rules. Obstacles leading to dislocation pile-ups are also accounted for. The deformation history is calculated in a linear incremental manner. Plane-strain boundary value problems are solved for a solid with edge dislocations on parallel slip planes, considering both monophasic and composite materials. The results show a peak in the shear stress versus shear strain curve followed by a plateau where the material deforms steadily. The plateau is associated with the localization of dislocation activity on isolated systems. The results for composite materials are compared with solutions obtained using a phenomenological continuum slip characterization of plastic flow.The paper presents a method for solving small-strain plasticity problems using a discrete dislocation model. The dislocations are represented as line defects in a linear elastic medium, and the solution is expressed as the superposition of the infinite-medium solution for the dislocations and a complementary solution that enforces boundary conditions on the finite body. The complementary solution is obtained from a finite-element solution of a linear elastic boundary value problem. The lattice resistance to dislocation motion, dislocation nucleation, and annihilation are incorporated into the formulation through constitutive rules. Obstacles leading to dislocation pile-ups are also accounted for. The deformation history is calculated in a linear incremental manner. Plane-strain boundary value problems are solved for a solid with edge dislocations on parallel slip planes, considering both monophasic and composite materials. The results show a peak in the shear stress versus shear strain curve followed by a plateau where the material deforms steadily. The plateau is associated with the localization of dislocation activity on isolated systems. The results for composite materials are compared with solutions obtained using a phenomenological continuum slip characterization of plastic flow.