The Birnbaum-Saunders distribution has received some attention in the statistical literature since its inception. The univariate Birnbaum-Saunders distribution has been used quite effectively in analyzing positively skewed data. Recently, bivariate and multivariate Birnbaum-Saunders distributions have been introduced in the literature. In this paper we propose a new generalization of the multivariate (p-variate) Birnbaum-Saunders distribution based on the multivariate skew normal distribution. It is observed that the proposed distribution is more flexible than the multivariateBirnbaum-Saunders distribution, and the multivariate Birnbaum-Saunders distribution can be obtained as a special case of the proposed model. We obtain the marginal, reciprocal and conditional distributions, and also discuss some otherproperties. The proposed p-variate distribution has a total of 3p + parameters. We use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters. One data analysis has been performed forillustrative purposes.