Direct methods of solution for solving nonlinear Volterra integral and integro-differential equations are inherently serial and therefore have not received much attention for use on a parallel computer. It is possible, however, to make significant gains in speedup by employing some novel approaches to existing methods. It can be observed that when approximating the integral term, all approximations up to and including the kth step in the interval can be evaluated at the same time. The resulting algorithm is described here and several numerical examples illustrate the results. With the four-processor multicomputer utilized, speedups of 3 to 4 were realized.