Continuum peridynamics provides an alternative to continuum mechanics. However, peridynamics is more general because it allows cracks to emerge. However, peridynamics requires further discretization to be implemented on a computer. Peridynamics assumes the material space is a continuous Cartesian real space. In contrast, in this paper we assume the material space is a discrete Cartesian integer space, defining a regular lattice of material particles, and proceed to develop the state-based peridynamic lattice model (SPLM). With the SPLM, the forces between neighboring particles are characterized by the force state, T, and the stretches between particles are characterized by the deformation state, Y. The material model arises from a peridynamic function relating the force state to the deformation state. With the SPLM, continuous deformations, elasticity, damage, plasticity, cracks, and fragments can be simulated in a coherent and simple manner. With the ongoing increase in computational storage capacity and processing power, the SPLM becomes increasingly competitive with more traditional continuum approaches like the finite element method.