The pairing instability in the Hubbard model for a 2D lattice is examined by using the perturbation approach. The two-particle interactions in both singlet and triplet channels are considered. The kernel of two-particle interactions in the charge and spin channels and the irreducible charge and spin response functions are also obtained. The expansion of the equation for the t-matrix over the Legendre polynomials is used to find the singularity in the harmonics of the t-matrix equation for different orbital momenta λ. A pairing instability in the singlet channel can be seen either in the state λ = 0 (s-wave) or in the state with λ = 2 (d-wave). T c for both s- and d-wave states is calculated by using the pole condition of the t-matrix. The strongly anisotropic s-wave state near the antiferromagnetic or SDW instability resembles the d x 2−y 2 wave symmetry.