A simple high power free electron laser resonator is extremely sensitive to the misalignment of end mirrors because of its long cavity length and the small transverse dimension of the gain region. Two schemes, mode-rotation and intracavity beam divergence, have been considered to improve the alignment sensitivity. The effects are studied analytically and numerically for a free electron laser ring resonator. The results show that neither the intracavity beam divergence scheme nor the mode-rotation scheme can reduce the alignment sensitivity, but the mode-rotation scheme provides significant improvement in the brightness of laser output.