To investigate the relationship between former strain and stability of a superconducting solenoid, a test coil was constructed and was applied to a training test. In this test, time dependences of the former circumferential strain ε_θ and quench currents I_q were measured. I_q decreased at the next quenches, when the residual compressive strain ε_θ^R of the former occurred at the previous quench. Especially when the coil emerged from boiling helium at a quench, the absolute value of ε_θ^R increased, and I_q remarkably decreased at the next quench. These occurrences of ε_θ^R could be ascribed to fast change of the Lorents force and thermal condition at the quenches.