When　exposed　to　an　external　solvent,　a　dry　polymeric　network　imbibes　the　solvent　and　undergoes　large　deformation.　The　resulting　aggregate　is　known　as　a　hydrogel.　This　swelling　process　is　diffusion　driven　and　thus　results　in　differential　swelling　during　transient　swelling.　When　subjected　to　external　geometrical　constraints,　such　as　being　rigidly　fixed　or　attachment　to　a　compliant　substrate,　wrinkles　have　been　shown　to　appear　due　to　mechanical　instabilities.　In　the　case　of　free　swelling,　there　are　no　external　constraints　to　induce　the　instabilities　accounting　for　wrinkling　patterns.　However,　during　the　transient　swelling　process,　the　swelling　differential　between　the　gel　on　the　exterior　and　the　interior　causes　compressive　stresses　and　gives　rise　to　mechanical　instabilities.　It　is　also　observed　that　the　time　dependence　of　the　swelling　profile　causes　the　wrinkles　to　evolve　with　time.　In　this　work,　we　investigate　this　interesting　phenomenon　of　transient　wrinkle　mode　evolution　using　the　finite　element　and　state-space　methods.　From　our　simulations　and　prediction,　we　find　that　there　is　an　inverse　relation　between　critical　wave　number　and　time,　which　has　earlier　been　observed　in　experiments.