This paper presents a numerical study of the effects of different shapes of deterministic microasperities in sliding surface lubrication when hydrodynamic films are found. Positive (protruding) and negative (recessed) asperities of constant height (depth) are considered with circular, square, diamond, hexagonal and triangular cross-sections. Of particular interest is the impact of asperity/cavity cross-sectional geometry on friction and leakage, which has importance in sealing applications. The results indicate that the friction coefficient is insensitive to asperity/cavity shape, but quite sensitive to the size of the cross-section. By contrast, leakage rates are found to be quite sensitive to both cross-sectional shape and size, with triangular asperities giving the smallest leakage rate and square asperities giving a largest leakage rate. The minimum coefficient of friction for all shapes is found to occur at an asperity area fraction of 0.2 for positive asperities and 0.7 for negative asperities. Finally, the results indicate the existence of a critical asperity area fraction where the performance curves for positive and negative asperities cross over. These cross-over points are identified for friction coefficient and leakage rate.