Hydrogels possess exceptional mechanical properties and biocompatibility, making them widely used in contemporary bioengineering. Specifically, in the development of wearable and implantable health monitoring devices as well as drug delivery systems, hydrogels are utilized to enable precise control over the transport of solutes. Nonetheless, predicting the distribution of substances within hydrogels still poses a significant challenge due to the complex interplay between the movement of water content, migration of solutes, and deformability of the hydrogel polymer network, which presents challenges to theoretical modeling. Our work introduces a numerical model that addresses the movement of water and solute within a flexible hydrogel, accounting for evaporation and/or moisture absorption at the boundary. The model solves for water saturation, solute concentration, and hydrogel deformation iteratively at each time step while computing the boundary movement velocity based on the transport process. By comparing the modeled results of geometry deformation and water and solute distributions during evaporation with our experiments, we demonstrate the accuracy and applicability of our proposed model. This capability to precisely analyze water and solute concentrations in deformable and nonuniform hydrogel environments paves the way for advancements in biosensing and drug delivery methods that rely on elastic porous materials.