Author states the condition of compatibility for the system $\xi_{ik} = \frac{1}{2} ( s_{ijk} + s_{kji} )$$(i,k = 1,2)$, where $\xi_{ik}$ denotes the strain tensor and $s_{i}$ the infinitesimal regular displacement vector. It is shown that the condition is unique and of the fifth order for general surfaces, i.e. for Riemannian two-dimensional varieties with variable curvature. In connection with the previous result, the author gives the solution of the well known yet unsolved problem of finding the general tensorial expression of the stresses $p_{ik}$, satisfying the indefinite equilibrium equations of continuous media $p_{ik}^{jk} = 0$$(i,k = 1,2)$.