The diameter growth of trees occurs by the progressive deposition of new wood layers at the stem periphery. These wood layers are submitted to at least two kinds of mechanical loads: maturation stress induced in wood during its formation , and the effect of the increasing self-weight. Interaction between growth and these loads causes mechanical stress with a particular distribution within the stem, called growth stresses. Growth stresses have technical consequences, such as cracks and deformations of lumber occurring during sawing, and biological consequences through their effect on stem strength. The first model for computing the field of stress inside a growing stem was set long ago by Kübler. Here, we extend these analytical formulations to cases with heterogeneous wood properties, eccentricity and bending stresses. Simulated profiles show reasonable agreement with measured profiles of released strains in logs. The particular shape of these profiles has consequences on stem bending strength. During bending in response to transient loads such as wind, most of the load is supported by outer parts of a stem cross section. The tensile maturation stress at this level increases the bending strength of the stem by delaying compression failure. Compressive stress in reaction to this tension does not reduce the bending strength because it is located near the centre of the stem and thus not loaded during bending, except if growth is strongly eccentric. Permanent bending stresses are concentrated at the mid-radius of the section, so that they do not cumulate with above-mentioned sources of stress. This smart distribution of stresses makes it possible that the stem is stronger than the wood it is made of, and that a growing stem can bend considerably more than its non-growing beam equivalent without breaking.