We determine the speed up of a recently developed parallel algorithm of solving of systems of linear ODEs on large parallel MIMD computers. The used numerical method for solving systems of linear ODEs is the Runge-Kutta method. An optimal number of subintervals (or processors) and an optimal number of equidistant points for an individual processor are assessed if a total interval is subdivided into N equal parts. It can be proven that the speed up is proportional to N ^1/2 .