In the previous papers [1, 2] the Peierls stiuctural ti-ansition in quasi-one-dimensional (QlD) c1ystals of the tetrathiofulvalene-teti·acyanoquinodimethane (TTF-TCNQ) type was investigated in a ID physical model of the c1ystal. The aim of this paper is to present the study of the Peierls ti·ansition in QlD organic c1ystals of TTF-TCNQ in a 2D physical model. A more complete c1ystal model is applied, which takes into account two the most important electron-phonon interactions. One interaction is of defo1mation potential type and the other is similar to that of the polaron. The ratios of amplitudes of the second interaction to the first one are characterized by the parameters y1 and r2, respectively. The equation for phonon Green function is deduced in the random phase approximation as a sum of diagrammatic ladder series of closed loops of electi·onic Green functions. The polarization operator as a function of temperature is calculated in the mentioned approximation for different values of the parameter d, where d is the ratio of the ti·ansfer energy in the direction ti·ansversal to conductive chains to the ti·ansfer energy along the conductive chains. The critical temperature of Peierls ti·ansition is dete1mined from the condition 1-ReTI(q,Q) = 0, when Q = 0, and qx= 1r, qy = 1r. Here TI(q,n) is the dimensionless phonon polarization operator. The polarization operator as a function of temperature, for different values of the parameters d and of the dimensionless Fenni momentum kF is calculated numerically. One graphic is presented in figure 1 (the polarization operator is named Polar). In this figure it is analyzed the case when the conduction band is half filled and kF = n/2. For these values of parameters the ti·ansition