In this paper an efficient ISAR image classification method is proposed based on Minimum Enclosed Circle based Shape Matrix (MECSM) representation of the targets. Initially, discordant ISAR images are processed to remove the noise and outliers. Next, an orientation alignment method is used to align the targets vertically to achieve rotation invariance. The Enhanced Minimum Enclosed Circle calculation method (EnMEC) finds the radius and centre of the Minimum Enclosed Circle (MEC) of the shape. Then, the classification of the targets is performed based on shape matrices generated by the MECSM representation method proposed in this paper. The MECSM representation overcomes the limitations of the conventional shape matrix representation such as the dependency of the shape matrix representation on centre of mass (COM) and maximum radius of the shape of the target. The MECSM representation also curtails the extraneous interpolations in representing the insignificant details around the target. Experimental analysis shows that the proposed method is robust against the deformations in the rudimentary silhouettes of the targets emanated from the complications abounded with ISAR image reconstruction and processing mechanisms.