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A new sampling design for populations whose units can be arranged as an N ×M matrix is proposed. The sample must satisfy some constraints: row and column sample sizes are set in advance. The proposed sampling method gives the same selection probability to all the sample matrices that satisfy the constraints.Three algorithms to select a sample uniformly in the feasible set are presented: an exact algorithm based on the multivariate hypergeometric distribution, an MCMC algorithm, and the cube method. Their performances are evaluated using Monte Carlo simulations. The designs for sampling elements in a given row or a given column are investigated and the single inclusion and joint selection probabilities under the proposed design are evaluated. Several variance estimators are proposed for the Horvitz-Thompson estimator of the population mean of the survey variable y and their performances are compared in a Monte Carlo study. A numerical example dealing with a creel survey of fishermen found at 9 sites over 36 days is presented.