Polymer gels are soft solids with thermodynamically semi-open features which enables the solvents to flow in and out of the gels. The volume of gels is coupled to deformation due to this unique feature. The imposition of strain or stress on gels drives a finite change in volume, and the resultant volume change influences the mechanical properties of the gels. Significantly less attention has been paid to the strain-induced volume change in the conventional mechanical testing of gels, because the characteristic time of this phenomenon (τ_sw) governed by diffusion process is considerably long for millimeter- or centimeter-sized gels, as compared to the experimental time scale represented by ⁻¹ or ω⁻¹ where and ω are the strain rate and angular frequency, respectively. The stress relaxation experiments in the long time scale (t ≈ τ_sw), and the tensile or compression experiments using extremely slow strain rates (⁻¹ ≈ τ_sw) reveal that Poisson's ratio and stress of gels in solvents are pronouncedly dependent of time, varying from the values for isovolumetric deformation to the values for the equilibrium deformation where the induced volume change saturates. The strain rates satisfying the relation ⁻¹ < τ_sw are easily attainable for micrometer- or nanometer-sized gels with markedly short τ_sw. The strain-rate-dependent mechanical properties of gels need to be considered in the design of soft actuators based on micro-fabricated gels and fine gel fibers. The volume of the gels is also coupled to other types of mechanical stimulus such as solvent flow and centrifugal force. The analysis of these phenomena enables us to evaluate various properties of the gels such as the frictional coefficient, osmotic bulk modulus and shear modulus. In this review article, we summarize the experimental and theoretical studies on a rich variety of phenomena caused by the strain-induced volume change under various types of strain and force such as constant uniaxial strain, sinusoidal force, ultraslow stretching and compression, solvent flow, and ultracentrifugal force.