A new boundary integral equation is derived directly for velocity gradients in a finite-strain clasto-plastic solid. These integral equations for velocity gradients do not involve hyper-singularities (when the source point is taken to the boundary) of the type found in the alternate case when the integral equations for velocities are differentiated to derive an integral relation for velocity gradients. Hence the new formulation obviates the need for a two tier system of computing the velocity gradients, which existed in the alternate case. A generalized mid-point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients. Moreover, a mid-point evaluation of the generalized Jaumann integral is used to determine the material increments of stress. The constitutive equation employed is based on an endochronic model of combined isotropic/ kinematic hardening finite plasticity using the concepts of a material director triad and the associated plastic spin. The problem of a thick cylinder under prescribed internal velocity is considered for illustrative purposes. The solution derived from the present formulation is compared with that of the standard formulation and the exact solution.