A class of p-variate generalized Laplace distributions is defined as a class of distributions with density functions of the form \[ f(x)= K_{p,\lambda}| \Sigma| ^{-1/2}\exp\{-[(x-m)^{'}\Sigma^{-1}(x-m)]^{\lambda/2}\}, \] where vector \(m\in R^p\), \(\Sigma\) is \(p\times p\) symmetric positive definite matrix, \(p\geq 2\), and \(\lambda >0\). This class includes multivariate versions of the normal, Laplace and uniform distributions and has deep interrelations with elliptically contoured distributions. A method of simulation is described and certain bivariate density plots are given.