A mathematical model for predicting the steady-state thermal performance of one-dimensional (cocurrent and countercurrent) multistream beat exchangers and their networks is developed and is solved analytically for constant physical properties of streams. By introducing three matching matrices. the general Solution can be applied to various types of one-dimensional multistream heat exchangers such as shell-and-tube heat exchangers. plate heat exchangers and plate-fin heat exchangers as well as their networks. The general solution is applied to the calculation and design of multistream heat exchangers. Examples are given to illustrate the procedures in detail. Based on this solution the superstructure model is developed for synthesis of heat exchanger networks,