Abstract A new approach is developed for linear peridynamics together with constitutive equations for isotropic and anisotropic materials. As a departure from the standard peridynamic theory, the linear constitutive equation in the form of micromodulus is determined by directly requiring the resulting peridynamic equation to converge to Navier's equation as the material horizon approaches 0 in the case of an isotropic material, and to a comparable elastodynamic equation in the case of an anisotropic material. As a result, new peridynamic governing equations complete with constitutive equations are obtained for isotropic as well as anisotropic elastic materials. As an application of the newly obtained peridynamic equations, a plane wave solution is analytically obtained and discussed, and dispersion curves are plotted for orthotropic peridynamic materials.