In recent times, soft matter has gained significant interest among researchers in the fields of biomechanics and biomedicine, especially in areas like soft robotics and biopolymers, due to its remarkable ability to undergo substantial deformations. Soft robotics often requires materials that can flexibly adapt to or mimic the movements of living organisms, requiring properties of flexibility and easy deformability. Biopolymers, naturally occurring in the human body, such as within brain tissue or blood clots, have gained attention due to their tendency to exhibit extensive deformation even under minimal loads. Consequently, there has been a growing emphasis on investigating stress-strain responses associated with these materials in recent years. This research particularly centers on a specific deformation phenomenon known as the Poynting effect. The Poynting effect is related to the transverse stress or strain response when subjected to simple shear, revealing that the application of simple shear strain does not solely result in simple shear stress. This intriguing phenomenon captures our attention, primarily because it challenges intuitive expectations. Within the scope of this thesis, we employ two distinct deformation gradient tensors to analyze stress-strain responses under two separate boundary conditions: constant gap and constant normal stress boundary conditions. We also introduce a methodology for predicting the sign of the Poynting effect under conditions of small yet finite strain. Finally, we validate our analysis through simulation experiments. We have modified Meng's original network-theory-based model, which is rooted in an energy density function derived from the force-extension relationship of a single chain. Our objective was to create a model with nearly incompressible properties in order to investigate the impact of compressibility. To determine the direction of the Poynting effect, we directly computed the stress and strain responses of a cube under shear forces. Later, we developed a method for predicting the direction of the Poynting effect without the need for precise stress and strain calculations. Our results demonstrate the successfulness of this prediction method. The simulation outcomes reveal a closer alignment of the four-variable tensor, suggesting that our chosen boundary conditions more closely resemble those used in numerical solutions. Additionally, it is worth noting that the specific geometries we employed in our study, namely the cylinder and cube, did not have a discernible influence on determining the direction of the Poynting effect, especially within the context of the selected model and material parameters.