The effects of the solar wind compression of the dayside Venus ionosphere are simulated numerically. The initial ionosphere is assumed to be in pressure equilibrium with the (shocked) solar wind at the upper boundary of the ionosphere. Composition, densities, and temperatures of ions and electrons in the ionosphere are chosen in accordance with Pioneer Venus data. A spherically symmetric Lagrangian hydrodynamic code using a two-fluid model of the ionosphere consisting of 0+ and electrons is employed to simulate the effects on the ionosphere of rapid changes in solar wind pressure. Sudden increases in solar wind pressure are found to generate shock waves in the ions that propagate from the ionopause downward into the ionosphere with velocities as high as 5 km/s. The effect of shock waves on ionospheric density profiles is dramatic with distinct 'ledges' developing in the ionosphere at the shock front. Comparison of density profiles from our simulation with select Pioneer Venus ion mass spectrometer data suggest possible agreement between shock produced ionospheric ledges resulting from rapid solar wind compression and observed ionospheric ledges.