An implicit finite-volume numerical scheme has been developed to solve the three-dimensional transport equations that govern the electroosmotic and electrophoretic phenomena. The scheme consists of solving the ion transport equation and electro-neutrality condition coupled with Navier-Stokes equations for fluid flow in a sequential fashion until convergence is achieved. This capability is used for accurate modeling of electrokinetic focussing and of sample injection in cross-channels, and band-broadening in microchips. The simulations show that sample injection using electrokinetic switching technique produces sample plug with a large tail which has been observed in experiments. The simulations also show the sample plug broadening due to turns in the separation channel.