Let $\widetilde{W}$ be a two-parameter, R^d-valued generalized Brownian sheet. The author obtains an explicit Bessel--Riesz capacity estimate for the images of a two-dimensional set under $\widetilde{W}$. He also presents the connections between the Lebesgue measure of the image of $\widetilde{W}$ and Bessel--Riesz capacity. His conclusions also
solve a problem proposed by J.-P.Kahane.