A simple and accurate formula to calculate the failure load of adhesive bonded single lap joints under shear load based on plastic-to-failure criterion is presented. For this purpose a new failure mechanism is proposed, in which it is assumed that there is a critical lap length at which the adhesive behavior is perfectly plastic along the lap length. Solution of the governing differential equation is obtained in the elastic and plastic ranges. Straightforward arrangements of the boundary and compatibility conditions yield an explicit formula for the critical lap length, and hence a closed formula for the failure load can be found. The failure loads using the proposed analytical solution are calculated and compared with published results obtained using the numerical Runge-Kutta fourth order with shooting method. The comparison shows that the analytical solution predicts failure loads for a carbon/epoxy adherend joint within a 3.5% error, and within 1.8 for a glass/epoxy adherend joint. Also the failure loads corresponding to the critical lap lengths are calculated using the derived closed formula and compared with the published results. The comparison shows that these failure loads accurately predict the plastic failure limit within 2.6% for a carbon/epoxy adherend joint and within 4.7% for glass/epoxy adherend joint, for lap lengths greater than the critical one. Example calculations presented in this paper show that the critical failure loads can be considered as a conservative prediction of joint failure since they are always less than the upper limit of the failure loads.