In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.