A model based on finite volume analysis is presented here for multistream plate fin heat exchangers for cryogenic applications. The heat exchanger core is discretised in both the axial and transverse directions. The model accounts for effects of secondary parameters like axial heat conduction through the heat exchanger metal matrix, parasitic heat in-leak from surroundings, and effects of variable fluid properties/ metal matrix conductivity. Since the fins are discretised in the transverse direction, the use of a fin efficiency is eliminated and the effects of transverse heat conduction/stacking pattern can be taken care of. The model is validated against results obtained using commercially available software and a good agreement is observed. Results from the developed code are discussed for sample heat exchangers.