The cellular microstructure of softwoods such as spruce may be approximated as an irregular two-dimensional honeycomb. The nine macroscopic elastic constants of the wood, regarded as an orthotropic continuum, are governed by the geometric configuration of this honeycomb, together with the intrinsic material properties of the cell walls. Simple modelling is developed to allow all nine of these constants to be estimated from detailed microscopic measurements of the cell geometry, using assumed values for the cell-wall properties. Account is taken both of the cell-to-cell variations in growth and of the larger-scale modulation of cell properties in the annual growth rings. Results based on study of four samples of Norway spruce show very encouraging agreement with published measurements, and allow the relative importance of various effects to be assessed quantitatively.