The J/$psi$ azimuthal distribution relative to the reaction plane has been measured by the NA50 experiment in Pb-Pb collisions at 158 GeV/nucleon. Various physical mechanisms related to charmonium dissociation in the medium created in the heavy ion collision are expected to introduce an anisotropy in the azimuthal distribution of the observed J/$psi$ mesons at SPS energies. Hence, the measurement of J/$psi$ elliptic anisotropy, quantified by the Fourier coefficient v$_2$ of the J/$psi$ azimuthal distribution relative to the reaction plane, is an important tool to constrain theoretical models aimed at explaining the anomalous J/$psi$ suppression observed in Pb-Pb collisions. We present the measured J/$psi$ yields in different bins of azimuthal angle relative to the reaction plane, as well as the resulting values of the Fourier coefficient v$_{2}$ as a function of the collision centrality and of the J/$psi$ transverse momentum. The reaction plane has been estimated from the azimuthal distribution of the neutral transverse energy detected in an electromagnetic calorimeter. The analysis has been performed on a data sample of about 100 000 events, distributed in five centrality or p$_{rm T}$ sub-samples. The extracted v$_{2}$ values are significantly larger than zero for non-central collisions and are seen to increase with p$_{rm T}$.