To predict the transient response of multipass plate heat exchanger, an analysis is presented based on an axial heat dispersion model in the fluid which takes deviation from ideal plug flow into consideration. The method can be utilised to simulate the exit temperatures for both the fluids for any given arbitrary temperature transient at inlets. The methods takes the 'phase-lag' inside the distribution port into consideration and analyse the multipass plate heat exchanger by considering it as an assembly of single pass plate heat exchangers. The solution technique for equal number of passes on both the sides is different from that for unequal number of passes on the two sides. Examples of computation for the response of 1-2 and 2-2 pass configuration have been presented. The 1-2 pass exchanger is solved by analysing successive modules of the heat exchanger. The 2-2 pass heat exchanger is required to be simulated by iterating the responses of two smaller heat exchangers to which it has been divided. The method involves a Laplace transformation with the temporal variable, solution in space domain and numerical inversion of Laplace transform back to the time domain. The results indicate the strong effect of axial dispersion in fluid on the transient response. The effect of number of plates and number of transfer unit has also been studied which brings out a comprehensive picture of responses of a multipass plate heat exchanger in transient regime.