This paper presents an analysis of dislocations in a simple cubic lattice based on Peierls' approximate method. The width of a dislocation is small, with displacements comparable to the interatomic distance confined to a few atoms. The shear stress required to move a dislocation in a perfect lattice is about a thousandth of the theoretical shear strength. The energy and effective mass of a single dislocation increase logarithmically with the size of the specimen. A pair of dislocations of opposite sign in the same glide plane cannot be in stable equilibrium unless they are separated by a distance of the order of 10,000 lattice spacings. If an external shear stress is applied, there is a critical separation at which they are in unstable equilibrium. The energy of this state is the activation energy for dislocation pair formation, depending on the external shear and being about 7 electron volts per atomic plane for practical stresses. The model considers a simple cubic lattice with a dislocation of edge type. The slip plane divides the crystal into two halves, symmetric about a vertical plane. The dislocation line is perpendicular to the slip plane. The energy of a single dislocation is calculated, and the solution is extended to a pair of dislocations in equilibrium under external shear stress. The energy of this system is the activation energy for dislocation pair formation. The properties of this idealized model are discussed in relation to real crystals. The governing equation for the displacement of a point on the surface is derived, and the solution for a single dislocation is presented. The energy of a dislocation in an infinite crystal is infinite, but in a finite crystal, it is of order μd² log L/d. The effective mass of a dislocation is also calculated. For a pair of dislocations, the solution is derived, and the energy is calculated. The energy of the system is the activation energy for dislocation pair formation. The energy depends on the external shear and is about 7 electron volts per atomic plane for practical stresses. The shear stress required to move a single dislocation is estimated, and the energy required to form a dislocation pair is calculated. The results are compared with previous estimates, and the assumptions made are discussed. The paper concludes that the properties of dislocations in real crystals are unlikely to differ greatly from those calculated, but the stress required to move a dislocation and the critical separation of two dislocations may be seriously in error.This paper presents an analysis of dislocations in a simple cubic lattice based on Peierls' approximate method. The width of a dislocation is small, with displacements comparable to the interatomic distance confined to a few atoms. The shear stress required to move a dislocation in a perfect lattice is about a thousandth of the theoretical shear strength. The energy and effective mass of a single dislocation increase logarithmically with the size of the specimen. A pair of dislocations of opposite sign in the same glide plane cannot be in stable equilibrium unless they are separated by a distance of the order of 10,000 lattice spacings. If an external shear stress is applied, there is a critical separation at which they are in unstable equilibrium. The energy of this state is the activation energy for dislocation pair formation, depending on the external shear and being about 7 electron volts per atomic plane for practical stresses. The model considers a simple cubic lattice with a dislocation of edge type. The slip plane divides the crystal into two halves, symmetric about a vertical plane. The dislocation line is perpendicular to the slip plane. The energy of a single dislocation is calculated, and the solution is extended to a pair of dislocations in equilibrium under external shear stress. The energy of this system is the activation energy for dislocation pair formation. The properties of this idealized model are discussed in relation to real crystals. The governing equation for the displacement of a point on the surface is derived, and the solution for a single dislocation is presented. The energy of a dislocation in an infinite crystal is infinite, but in a finite crystal, it is of order μd² log L/d. The effective mass of a dislocation is also calculated. For a pair of dislocations, the solution is derived, and the energy is calculated. The energy of the system is the activation energy for dislocation pair formation. The energy depends on the external shear and is about 7 electron volts per atomic plane for practical stresses. The shear stress required to move a single dislocation is estimated, and the energy required to form a dislocation pair is calculated. The results are compared with previous estimates, and the assumptions made are discussed. The paper concludes that the properties of dislocations in real crystals are unlikely to differ greatly from those calculated, but the stress required to move a dislocation and the critical separation of two dislocations may be seriously in error.