The quantitative model proposed here for nanoimprinting by thermoplastic compression molding is focused on bulk metallic glasses (BMGs), but it is also applicable to polymers and other thermoplastic materials. In our model the flow and pressure fields are evaluated using the lubrication theory, and the effect of molding pressure, BMG viscosity, and capillary pressure on the spatial distribution of nanoimprinted features is determined. For platinum-based BMG the theory that takes into account capillary pressure but no other surface stresses agrees very well with experimental results. For palladium-based BMG (prone to oxidation) the extended theory includes an additional threshold pressure required to break the oxide layer that forms on the BMG surface. Our analysis provides important insights into flow behavior of BMG supercooled liquids. In particular, a new method for measuring surface tension and viscosity of BMGs and evaluating the strength of the surface oxide layer is demonstrated.