This paper presents an investigation on finite time thermodynamic evaluation of Ericsson and Stirling heat engines. Finite time thermodynamics has been applied to optimise the power output and thermal efficiency of both engines, including finite heat capacitance rates of the heat source and sink reservoirs external fluids, finite time heat transfer, regenerative heat losses and direct heat leak losses from source to sink reservoirs. The presence of these effects causes irreversibilities and affects the performance of the Ericsson and Stirling heat engines using ideal or real gas as the working fluid/substance. It is found that both cycles with an ideal regenerator (epsilon (R) = 1.00) are as efficient as an endoreversible Carnot heat engine operating at the same conditions, but this is not practical because an ideal regenerator requires either infinite regenerator area or infinite regeneration time. It is also found that the regenerative heat losses, regenerator effectiveness and the direct heat leak losses do not affect the maximum power output of either heat engine. Some special cases are also described.