Nanoclays are considered as an ideal filler for polymer materials owing to their versatility, low cost, high aspect ratio, large surface area, cross-linking behavior and cation exchange capacity. When compared with conventional composites, clay/polymer nanocomposites exhibit enhanced diffusional barrier, fire retardant, ultraviolet resistant and mechanical properties. The elastic modulus reflects the ability of a material to resist elastic deformation and is thus an important parameter that characterizes the material mechanical properties. Its accurate prediction plays an important role in material design to tailor a material to suit a given application. A broad variety of analytical as well as numerical work has been performed to investigate the elastic modulus of clay reinforced polymer composites. The present paper carries out a review and comparison between various analytical models reported in the technical literature that take fundamentally different approaches for predicting the elastic modulus, namely, the Guth and modified Guth model, the Halpin-Tsai model and modified Halpin-Tsai model, the model by Ji et al., the Hui-Shia model, and the effective modulus model. Elastic modulus predictions from these models for clay/elastomer composites are contrasted and discussed taking into consideration experimental data from the technical literature.