Transverse anisotropy in softwoods is an important phenomenon of both scientific and industrial interest. Simple one-phase hexagonal honeycomb cell models for transverse moduli of softwoods are based on cell wall bending as the only deformation mechanism. In the present study, a two-phase annual ring model is developed and includes both cell wall bending and stretching as deformation mechanisms. The proportion of cell wall bending and stretching for different cases is analysed and the importance of stretching is confirmed. A two-phase annual ring model is presented based on fixed densities for earlywood and latewood. Such a model is motivated by the large difference in density between earlywood and latewood layers. Two-phase model predictions show much better agreement with experimental data than predictions from a one-phase model. Radial modulus is dominated by bending at low density and by stretching at high density. For tangential modulus, bending is more important at all densities.