Solar wind disturbances produced by relatively long-lasting solar flares are simulated numerically by using the single-fluid magnetohydrodynamic (MHD) equations with negligible dissipation. The computations are confined to the ecliptic plane of a spherically symmetric flow and are begun when an initial disturbance is introduced near the sun in the ambient solar wind. The velocity and density in the disturbances do not differ appreciably from the values obtained by using an ordinary fluid dynamic calculation, but the thermal pressure exhibits a marked decrease near the contact (or 'piston') discontinuity. A comparison with several MHD similarity solutions shows the advantages of the present analysis over the latter theory to be the following: (1) it yields a quantitative prediction of the azimuthally induced plasma flow, (2) it provides for removal of the nonphysical zero pressure at the contact surface, and (3) it allows more flexibility in the specification of initial conditions, which gives the present analysis greater utility in predicting plasma and magnetic data. Alternative initial disturbances, such as pulses in radial velocity or thermal pressure, produce multiple nonlinear variations of the density, thermal pressure, and magnetic field. Spatial and temporal variations of the thermal and magnetic energy densities are thereby indicated.