The time rate of settlement process in clay involves changes in excess pore water pressure (EPWP) with time. Exact solutions have been published for constant initial EPWP and other simple distributions. The finite differences methods are generally used in solving complex initial EPWP distributions. Such methods suffer from roundoff errors at each time increment and truncation errors proportional to the step size used. The explicit finite difference method produces stable solutions when proper time and depth increments are used. An innovative explicit finite difference model involving eigenvalues and eigenvectors is proposed that will permit arbitrary initial EPWP distributions and reduce roundoff errors. This method is numerically stable and convergent. Unlike traditional methods, the proposed solution will also eliminate the need to calculate the EPWP vector traditionally required at each time increment. Instead, the EPWP can be computed directly for any number of time increments.