On the basis of the notion of `strain shift induced by quenching' a continuum model is proposed to provide mechanistic insight into the formation of the residual stresses from quenching. An equation has been derived stating that for a homogeneous quenched body the residual elastic strain of each elemental volume is equal to the difference in the amount of plastic strain generated by the alternating odd and even strain shifts. Despite the widespread view, plastic yielding is neither necessary nor sufficient for the existence of residual stresses after quenching. The proposed model successfully rationalized the results from the computer simulations and the residual stress patterns after oil and water quenching of decarburized and non-decarburized cylindrical steel specimens. If the net plastic strain (the difference in the amount of plastic strain during the first and second strain shift) created in the thermal contraction region is greater than the net plastic strain created in the transformation region the axial residual stress at the surface of a quenched cylindrical specimen is compressive. The magnitude of the transformation stresses generated is inversely proportional to the width of the transformation temperature interval. It is established that the thermal stresses during quenching raise the martensite start temperature of the surface. An equation and a numerical model have been derived for determining the shift of the martensite start temperature caused by thermal stresses of large magnitude.