Mirrors with an on-axis hole have been traditionally regarded as a radiation outcoupling means, but can also be seen, at a first approximation, as grading of the mirror reflectance. Hole introduction, by itself, can drastically change the basic mode shape of the resonator. Changing the radius of the hole aperture of the mirror may result in a wider mode (super-Gaussian) or a nulling field at the mirror's centre. Use of on-axis holes in mirror can improve the matching between the lower loss mode and the gain medium, assuring a low-loss and efficient system. Diffraction effects due to the on-axis hole and the finite size of the mirror are analysed numerically in zero- and first-order cylindrical symmetry. The power amplitude distribution and the losses of the lowest-loss mode are calculated as a function of the physical resonator parameters. Experimental results are presented, confirming computed results. The dependence of the lowest loss mode on the physical parameters is shown for an empty stable resonator with different stability parameters. Two effects are emphasized: A general centre avoiding effect and the hole avoiding effect.