The P,T -odd Faraday effect (i.e., rotation of the polarization plane of light propagating through a medium in presence of the external electric field due to P, T symmetry violating interactions) is considered for several atomic species: Ra, Pb, Tl, Hg, Cs, and Xe. Corresponding theoretical simulation of P,T -odd Faraday experiment, with already achieved intracavity absorption spectroscopy characteristics and parameters, is performed. The results show that the magnetic dipole transitions in the Tl and Pb atoms as well as the electric dipole transitions in the Ra, Hg and Cs atoms are favorable for the observation of the P,T -odd Faraday optical rotation. The estimation of the rotation angle of the light polarization plane demonstrates that recently existing boundaries for the electron electric dipole moment can be improved by one-two orders of magnitude.ThO molecule (d e < 0.87 × 10 −28 e cm [12], d e < 1.1 × 10 −29 e cm [13]), and HfF + molecular ion (d e < 1.3 × 10 −28 e cm) [14] (e is the electron charge). However, to extract the eEDM values from the experimental data, the accurate calculations of the eEDM enhancement coefficients are required. These calculations were performed for Tl in [15][16][17][18], for YbF in [19][20][21][22], for ThO in [23][24][25][26] and for HfF + in [27][28][29][30].The optical rotation experiments to study spatial parity nonconserving (PNC) effects (that is to say, the rotation of the light polarization plane in atomic or molecular vapors that do not possess natural optical activity) were originally proposed in [31] for hydrogen atom where parity nonconservation is very small. After a while in 1974 a new proposal with the Bi atom was discussed [32]. In addition, the first successful optical rotation experiment on the PNC effect observation in Bi was performed in 1978 [33]. What concerns the experiment on the search for the P,T symmetry violation effects, all of them up to now are advancing in two directions: the shift of the magnetic resonance in an external electric field [10] and the electron spin precession in an external electric field [11][12][13][14]. Since the recent experimental bound for the eEDM is still 9 orders of magnitude larger than the maximum theoretical prediction of the SM, other methods of the observation of such effects are of interest. The optical rotation in an external electric field can be referred to as the P,T -odd analogue of the Faraday effect (the latter is the optical rotation in an external magnetic field). Unlike the ordinary Faraday effect, in an external electric field such optical rotation can arise only due to the violation of P and T symmetries. In [34] the possible existence of such an effect was discussed. Measurement of the eEDM using the Faraday rotation technique was suggested in [35]. Different theoretical and experimental studies were directed to observe it (see, e.g., short review [36]). Recently, in [37] the possibility of the P,T -odd Faraday effect observation by means of the cavity-enhanced technique and intracavity absorption spect...