The plant cell wall is treated as a two phase fibre composite material in which the fibres are dispersed, in an isotropic matrix, in the plane of the cell wall with an angular distribution f(θ). If f (θ) can be represented by a gaussian it is shown that the elastic stiffness constants of the cell wall can be easily evaluated. The theory is applied to a model of the earlywood of Pinus radiata and the theoretical variation of the longitudinal Young's Modulus with mean fibrilar direction is compared with that determined experimentally.