Numerical models of the initial deformation of extending continental lithosphere have been computed to investigate the control of pre-existing thermal and mechanical heterogeneities on the style of deformation. The finite element technique was used to calculate deformation with a viscoelastic-plastic model for the lithosphere. Initial heterogeneities tested included a variety of thermal anomalies, anomalous fracturing in the upper crust, and anomalous crustal thickening. Deformation is strongly localized by thermal, mechanical, or compositional heterogeneities. The style of initial deformation is controlled by the depth and width of the heterogeneities. Shallow weakening of the lithosphere causes broad uparching of the lithosphere in the early stages of deformation due to elastic bending stresses caused by non-uniform extensional deformation. Deeper weakening of the lithosphere has the opposite effect. The width of the zone of necking is closely controlled by the width of the initial heterogeneity, with a minimum width controlled by the layer structure of the model. The continuum-mechanics formulation of the models prevent the reproduction of fault details in the models, but general features of extensional style are indicated. Thermal heterogeneities are most effective in controlling deformational style: broad zones of high strain are predicted by wide thermal anomalies penetrating up to the Moho or shallower; brittle, low-strain extension is predicted by models with deeper, narrower thermal anomalies. Deep-penetrating low-angle faults are not required to reproduce the broad lithospheric deformational styles observed in lithospheric extension.