A method to determine lower and upper bound limit loads called interpolated moduli adjustment technique (IMAT) is proposed in this article. This method is based on iterative linear elastic analyses and is applied to several test cases of practical interest. IMAT fully conforms to the classical lower and upper bound theorems. In all the cases, the upper and lower bound limit loads converge, thereby establishing the robustness of the technique. The results from IMAT correlate with nonlinear finite element analysis consistently within 3%.