The possibility is discussed of detecting $P$-odd weak interaction of the electrons with the nucleus from effects of interaction of atoms with resonance radiation. The requirements of accuracy of three types of experiments are discussed: 1) directly measuring the difference of absorption cross sections for right-handand left-hand-polarized light; 2) measuring rotation of the plane of polarization; and 3) measuring the splitting of the intrinsic frequencies of an optical resonator. The calculated values of the expected effect are tabulated for the atoms that are most promising from the experimental standpoint, together with other spectroscopic characteristics of the transition.