Methods are presented for calibrating the local elastic properties of tow-scale material domains in virtual specimens of textile composites. A model of the tow geometry is calibrated using 3D tomographic data via previously published methods. The local elasticity is defined to vary with the local tow orientation and fiber volume fraction within tows. The accuracy of the tow geometry is assessed by comparing the surface geometry of virtual specimens with an alternative data source, viz. topographical data obtained by digital image correlation. Calibration of the elastic constants is validated by comparing measured surface strain distributions with computed strain distributions. An approach is also presented for extending the model to the non-linear regime, by simulating the response of virtual specimens in which the bonds between abutting tows are broken and the resulting fracture surfaces are frictionless. The latter results yield a better match to the measured strain distributions.