A physical model and related formulas for the calculation of small-signal gain and phase shift in a severed injected-beam crossed-field amplifier are presented in this paper. The analysis is based on the linear theory of thin beam CFA with the space charge effect included. In the analysis the space charge effect as well as the circuit loss and the velocity difference between electrons and undisturbed waves are considered."Sever Drop"and "Sever Phase Shift" are introduced in formulas to represent the effect of the sever.The"Sever Drop"can be of a negative value due to the Diocotron effect in the sever. The influence of sever location on the gain is also analyzed based on a zero-length sever model.