The entry problem in plane laminar magnetohydrodynamic flow is solved numerically for various values of the pertinent parameters describing the flow. The channel configuration is a parallel‐plate channel which has the Hartmann profile for its fully developed velocity flow. The equations are placed in a finite difference form to enable the essential nonlinearities of the principal equations to be used in the solution of the problem. Velocity, temperature, and pressure curves are presented from the results of computational work.