There are different stress–strain definitions to measure the elastic modulus of hydrogel materials. However, there is no agreement as to which stress–strain definition should be employed. This study is aimed to carry out a comparative study on different results that are given by the various definitions of stress–strain and to recommend a specific definition when testing hydrogel materials. The prepared gelatin hydrogels are subjected to a series of compression tests to measure their mechanical properties. Three stress definitions (second Piola–Kirchhoff stress, engineering stress, and true stress) and four strain definitions (Almansi–Hamel strain, Green–St Venant strain, engineering strain, and true strain) are used to determine the elastic modulus and maximum stress and strain. The highest nonlinear stress–strain relation is observed for the Almansi–Hamel strain definition and, as a result, it may overestimate the elastic modulus at different stress definitions (second Piola–Kirchhoff stress, engineering stress, and true stress). The Green–St Venant strain definition fails to address the nonlinear stress–strain relation using different definitions of stress and invokes an underestimation of the elastic modulus values. Engineering stress and strain definitions are only valid for small strains and displacements which make them impractical when large deformation is expected. The results also show that the effect of varying the stress definition on the maximum stress measurements is significant but not when calculating the elastic modulus. It is of vital importance to consider which stress–strain definition is employed when characterizing the mechanical properties of hydrogel materials. The results suggest the application of the true stress–true strain definition for characterization of the hydrogel material mechanics since it gives more accurate measurements of the material’s response using instantaneous values.