Combustion model structures based on Vibe functions are outlined and investigated in this work. The focus of the study is the use of such model structures for estimation of diesel combustion properties by reconstructing in-cylinder pressure from measurements of crankshaft torque. Investigated combustion properties include the start and phasing of the combustion as well as maximum values of the in-cylinder pressure and its derivative. The accuracy associated with the proposed estimation method is evaluated using ideal torque data, i.e. torque calculated from in-cylinder pressure, that is generated using both simulations and experiments. The results indicate that the uncertainty associated with the estimation of a selected combustion property tends to increase if that property is located close to TDC, where the signal-to-noise ratio is low for a torque signal. The results also show that the ideal torque based estimation of combustion phasing and maximum in-cylinder pressure generally is very accurate while the estimation of start of combustion and the maximum in-cylinder pressure derivative suffers more from disturbances and model imperfections.