A damage evolution of adhesively bonded butt joints with a rubber-modified adhesive has been investigated under cyclic loading. An isotropic continuum damage model coupled with a kinetic law of damage evolution was applied to the butt joint. To solve the kinetic law, analytic and numerical methods were tried: the former solution was derived with some simplifications and the latter one was derived rigorously without simplications. On comparing the analytic solutions with the numerical ones, it was confirmed that differences in the two solutions were small. Furthermore, the estimated S-N curves based on the analytic equation agreed well with experimental data.