The dynamics of expanding domes of isothermal lava are studied by treating the lava as a viscoplastic material with the Herschel–Bulkley constitutive law. Thin-layer theory is developed for radially symmetric extrusions onto horizontal plates. This provides an evolution equation for the thickness of the fluid that can be used to model expanding isothermal lava domes. Numerical and analytical solutions are derived that explore the effects of yield stress, shear thinning and basal sliding on the dome evolution. The results are briefly compared with an experimental study. It is found that it is difficult to unravel the combined effects of shear thinning and yield stress; this may prove important to studies that attempt to infer yield stress from morphology of flowing lava.