Sheet metals, due to their broad applications in aerospace industries, are one of the most important issues in metal forming researches. One of the useful methods in identifying forming limit and preventing sheets from tearing is the use of FLC curve. In addition to the forming limit, this curve presents a boundary for allowable strain. This paper relies mainly on the accuracy and broad application of this method. After reviewing the history of formability limit curves specially the theory suggested by Marciniak and Kuczynski known as M-K, a new model, taking in to account the shortcomings of the above-mentioned theory, is presented which is in line with the results of that theory. In this theory, like M-K theory, a thin plate with non-homogeneity is selected as a decrease in gradient thickness with a sinusoidal function and is under a 2D stress. By analytical study, finally, a differential equation is achieved and the result in the range of positive strains (stretched zone) is the same as the result of M-K theory, and in the range of negative strains (tension zone) completes the FLC curve. The results of applying this equation on two alloys with the hardening exponents of 0.4 and 0.24 show the accuracy of this equation.