We study the effect of applied strain as a physical control parameter for the phase transitions of Ca(Fe1−xCox)2As2 using resistivity, magnetization, x-ray diffraction, and 57Fe Mössbauer spectroscopy. Biaxial strain, namely, compression of the basal plane of the tetragonal unit cell, is created through firm bonding of samples to a rigid substrate via differential thermal expansion. This strain is shown to induce a magnetostructural phase transition in originally paramagnetic samples, and superconductivity in previously nonsuperconducting ones. The magnetostructural transition is gradual as a consequence of using strain instead of pressure or stress as a tuning parameter.