The elasticity problem for an anisotropic homogeneous medium containing an isolated crack is reduced to 2D-integral equation for the crack opening vector. For an elliptical crack subjected to a polynomial external stress field, the polynomial conservation theorem is proved. For an elliptical crack subjected to a constant external field, determination of the crack opening vector and the stress intensity factors at the crack edge are reduced to calculation of 2D improper integrals. For isotropic host media, these integrals are expressed in terms of complete elliptic integrals. The conductivity problem for a crack is considered.