Multistream plate fin heat exchangers (MSPFHEs) are vital components of large cryogenic systems. A computer program is developed for layer by layer analysis of thermal performance of MSPFHEs and is validated against the published experimental results. Cross layer conduction between the streams in non-adjacent layers and heat transfer between the streams in consecutive layers are computed using analytical formulation. This avoids the need of fin discretisation along its height. Heat exchanger is discretised along the flow direction to take care of the effects of axial heat conduction and material property variation. Finite difference method (FDM) is used to convert the energy balance equations into a system of linear algebraic equations, which are solved iteratively. The developed computational method is found to be of adequate accuracy, capturing all the effects and can be used for MSPFHE design for cryogenic systems.