The task of determining optimal estimates of a flat’s structural element spatial orientation angles is considered. Its initial data are the measured coordinates of points on its surface. The known methods of solving are based on minimizing the quadratic function of the distances between the plane and the points. The reasons for the decrease in the accuracy of the plane parameters estimates in these techniques are analyzed. The necessity of taking into account additional constraints on them at solving the mentioned problem is justified. Three new approaches to finding estimates of the azimuthal and horizontal angles of the plane orientation are proposed: based on the Lagrange multiplier method (considering the normalization of the coefficients of the plane canonical equation); by direct finding the minimum of the function for measuring discrepancies at the desired angles; and using the eigenvectors of the covariance matrix for points spatial coordinates. The ratios for calculating the standard errors of the required orientation angles are given. A comparative analysis of the known and three new ways of solving the problem, carried out using the results of calculations, illustrates the advantages and expediency of using newly developed approaches