Approximation properties of multivariate sampling-type expansions with matrix dilation are studied. In particular, we investigate the expansions whose coefficients are the sampled values of some linear combination of the approximated function f and its derivatives. The error estimation in L_p-norm, 2 ≤ p ≤ ∞, is given in terms of the Fourier transform of f for this case. Another class of expansions includes those whose coefficients are integral averages of f near the nodes. The error estimation in L_p-norm, 1 < p < ∞, is given in terms of the moduli of smoothness of f for this case.