<p>Having been studied for a long time, simple and pure shear deformation models are well known in elasticity. For small deformations, these two shear models differ only by a rigid rotation. On the contrary, for large deformations, the two models do not differ only by a rigid rotation. Therefore, in the latter situation, one cannot expect both models to fit the same constitutive properties for a prescribed form of the stored energy function. The kinematic and static differences between the two shear models, as well as their inadequacies for simulating experimental evidences, are discussed in this paper. To overcome these critical issues, a study was developed, which led quite naturally to the definition of a new shear deformation model, here called <i>purely angular shear</i>, based on the direct extension of the linearized pure shear model. The new model, characterized by a simple and immediate physical meaning, is particularly suitable for matching experimental tests.</p>