Summary: In this work mixture models are proposed for the construction of bivariate and multivariate circular distributions. These mixture models allow ease of generation on a computer for Monte Carlo simulation studies. The mixture model method is exemplified by considering the well-known von Mises distribution. Two bivariate mixed von Mises distributions are derived and their Fourier series representations, joint trigonometric moments and limiting cases are considered. A possible application to model real-life situation is also discussed.