This paper shows how the transient response of parallel heat exchanger with finite wall capacitance may be calculated by analytical method. Making usual idealizations for analysis of dynamic behaviour of heat exchanger, the model is based on three local energy balance equations which are solved by using the Laplace transform method for step change of the primary fluid inlet temperature. The solution are found in the case of constant initial conditions and expressed in explicit analytical form in terms of the number of transfer units, heat capacity ratios, heat transfer resistance and flow capacitance ratios. Present solutions are valid in case where fluid velocities are different or equal and finite or infinite. The solutions can be very suitable for mathematical modelling systems containing such types of heat exchangers.