[en] The purpose of the study is to prove the possibility of using the P-3 approximation in the spherical harmonics method for calculating the thermal neutron fields in complex cells of nuclear reactor polylattices with channels with almost ''black'' blocks. Neutron fluxes and nuclear reaction velocities are calculated for the RBMK and MR type reactor cells in one-velocity approximation using the Monte Carlo and spherical harmonics methods as well as the methods of characteristics and first collision probability. The EXAMP, P3F, REKINUR and MK programs are used for calculations. 3 variants, namely the uniform RBMK type lattice with homogenized channels, the double lattice of the MR type with homogenized channels and the double lattice of the MR type with multiring channels, are investigated. The analysis of the obtained results shows that for the uniform RBMK type lattice and double MR type lattice with homogenized channels a satisfactory agreement of calculational results for all above methods is observed. In the case of double the MR type lattice with multiring channels maximum differences in neutron flux values obtained using the P-3 approximation and the Monte Carlo method at given boron absorption cross sections in the reactor control system channel and various lattice pitches constitute respectively 1% for the absorbing section of reactor control system channel, 2% for multiplying zones of the fuel channel, 6% for graphite, 11% for water zones. It is concluded that the calculational error for the P-3 approximation as compared with that for the Monte Carlo method is practically independent of lattice pitch and boron absorption cross section value