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Two-dimensional hydrodynamic calculations of SN 1987A (Arnett, Fryxell, and Muller 1989) have been confirmed and extended. A systematic sequence of calculations, differing only in resolution, is presented in order to permit differentiation between physical and numerical effects. This sequence also makes possible comparison with other work done with different numerical techniques. Shortly after the shock reaches the surface of the presupernova, the spherical symmetry of the mantle is severely fractured as a result of Rayleigh-Taylor instabilities. No special asymmetry in the explosion is required. This fracturing appears long before significant decay of ^56^Ni occurs. The presence of the instability seems to be rather insensitive to the initial presupernova structure (provided it is reasonably accurate). The amount of mixing of various elements is determined by including 10 separate fluids in the calculations enabling us to determine the distribution of each element in velocity space. The amount of mixing and clumping is somewhat sensitive to the choice of seed perturbation. However, it appears that perturbations of physically reasonable amplitude will provide sufficient mixing and clumping to explain the earlier than expected observations of X-rays and y-rays and the shape of the light curve. The velocities of heavy elements are lower than observed for an explosion energy of 1.0 x 10^51^ ergs, but are interestingly close for 2.0 x 10^51^ ergs, and will increase after ^56^Ni decay heats the inner regions. The degree of clumping obtained would also affect estimates of mass from modeling the light curves of SN Ib.