  We present the classical Wagner construction from 1935 of the curvature
tensor for completely nonholonomic manifolds in both invariant and coordinate
way. The starting point is the Shouten curvature tensor for nonholonomic
connection introduced by Vranceanu and Shouten. We illustrate the construction
on two mechanical examples: the case of a homogeneous disc rolling without
sliding on a horizontal plane and the case of a homogeneous ball rolling
without sliding on a fixed sphere. In the second case we study the conditions
on the ratio of diameters of the ball and the sphere to obtain a flat space -
with the Wagner curvature tensor equal zero.
