Open laser resonators based on the self-imaging property of periodic fields (the Talbot effect) are studied theoretically and experimentally. Numerical simulations in one-dimensional cartesian geometry have revealed that the fundamental mode losses in such resonators decrease as the number of periods is increased. Convergence to a fundamental mode takes place in a few round-trips (< 10) with a moderate number of periods (< 20). Experimental tests with a TEA-CO2 laser have verified the periodic and self-imaging properties of the emitted field. An equivalent self-imaging configuration for cylindrical symmetry is proposed.