The work introduces a mathematical framework and a corresponding implementable algorithm to automatically perform Volterra analysis of weakly nonlinear circuits. The analysis is based on the general composition rule for multivariate Volterra operators. The approach is amenable to the design of efficient computer algorithms as it just involves multiplication and inversion of sparse matrices and Kronecker products. An algorithms to construct the higher-order device matrices from elemental information about the circuit's topology and nonlinear device characteristics is given. The example of a single MOSFET-transistor amplifier is used to illustrate the method.