AbstractThis review focuses on the novel features of nonlinear elasticity for a range of gels and elastomers that were recently revealed through experiments using various types of strain such as uniaxial and biaxial stretching. Particular emphasis is placed on the magnitude of the cross‐effect of strains in different directions which can be characterized by unequal biaxial stretching. The studied materials include (1) markedly swollen hydrogels with a water content of 98%, (2) tetra‐arm poly(ethylene glycol) (Tetra‐PEG) gels with nearly uniform network structures without entanglement couplings of network strands, (3) slide‐ring gels with movable crosslinks along network strands and (4) elastomer foams with low densities of polymer solids. The magnitude of the cross‐effect of strains reflects the structural features of networks and crosslinks as well as bulk compressibility for each material. We also summarize recent results on strain‐driven swelling and the accompanying force reduction phenomena under various types of stretching. Remaining issues to be investigated are presented on the basis of existing results. © 2016 Society of Chemical Industry