A two-dimensional code is developed for simulating the nonuniformly expanding plasma sheath when a negative potential is applied to a two-dimensional target immersed in a plasma. The code uses fluid equations for the cold, collisionless ions coupled with the Boltzmann relationship for the electrons and Poisson’s equation. The evolution of the sheath at a square target is simulated numerically. The nonuniformity of the incident dose and the angular distribution of the ions striking the surface near the comer are calculated. The incident dose is higher near the comer of the square target but has its maximum value at a slight distance from the comer. In addition, the angle at which the ions strike the surface is more oblique near the corner and the area over which the oblique angle occurs broadens as the sheath grows.