This Article presents a bivariate extension of the quadrature method of moments for solving two-dimensional batch crystallization models involving crystals nucleation, size-dependent growths, aggregation, and dissolution of small nuclei below certain critical size in a dissolution unit. In this technique, orthogonal polynomials of lower order moments are used to find the quadrature abscissas (points) and weights. Several benchmark problems with different combinations of processes are considered in this Article. The accuracy and efficiency of the proposed method are validated against the analytical solutions and the high-resolution finite volume scheme. Excellent agreements were observed in all test problems. It was found that the current method is very efficient and accurate as compared to the high-resolution finite volume scheme.