Double salient pole structure of Switched Reluctance Motors (SRMs) yields minimum and maximum points in the inductance profile. Minimum and maximum inductances directly affect energy conversion capabilities of a given design. Estimating the maximum inductance is a relatively simple process, even if MMF drop in the magnetic steel is not ignored. However, minimum inductance estimation is much more difficult task due to the uncertain path of airgap magnetic field which is dominated by fringing between rotor and stator poles. A new approach is proposed in this paper to estimate minimum inductance (Lmin) of SRM. Finite Element Method (FEM) and Artificial Neural Network (ANN) are employed together for estimation. The data collected by GEMINI electromagnetic finite element software are used to train ANN. Trained ANN is tested by a test data set. Total estimation error in the test set is observed to be less than 2%.