Stirling engines are promising candidates for applications where air breathing engines cannot be used. Self contained engines capable of operating independently of the environment are required to convert thermal energy into electric power, or to perform other necessary functions. These are ideally suited for power generation onboard spacecrafts with radioisotope heat source. These engines can power interplanetary missions to Mars and beyond. The problem of parametric analysis, sensitivity and numerical optimization of Stirling cycle engine is discussed and applied to a specific example of a 2kWe free piston Stirling engine. Stirling cycle simulation programs are generated with emphasis and adaptations peculiar to free piston design for space use. Design algorithms are generated in MatLab and optimization toolbox is used for the parametric analysis adopted in this thesis. A free piston beta Stirling engine with a linear alternator configuration has been studied for the interdependency and performance effects of various important operational parameters. The analysis has been carried out in order to optimize the primary parameters, weight vis a vis envelope (length and diameter) and stroke of the engine, to make it suitable for space use. The major cycle parameters considered are operating pressure, linear speed, dead space ratio and swept volume ratio, classified as secondary parameters. The whole analysis has been carried out at a cycle temperature ratio of 0.4 for a heat source temperature of 873 K, typical of a radioisotope heat source. The optimization is carried out for the defined design requirements viz. envelope of 50 × 50 cm , stroke of less than 10 cm, and heat source temperature of 873 K. The process of parametric optimization of the primary parameters viz engine envelope and stroke are carried out with respect to the secondary parameters. Iterations are carried out on the design programs in MatLab. The results indicate that the three primary parameters have a different set each, of the secondary parameter values when optimized to the design requirement. The fmincon solver of MatLab in the optimization tool box is selected in order to validate the optimization results. The solver is used to find a minimum of a constrained nonlinear multivariable function defining the primary parameters. The results obtained concur with the optimization results generated by the design algorithm. Further, the interdependency amongst the primary and secondary parameters is studied by generating MatLab plots for all possible combinations among the various parameters. The effect of variations in the pressure and linear speed on the system envelope and stroke are more pronounced at lower range values of the pressure and speed and the variations of the primary parameter values are constant at higher ranges. The effect of dead space ratio and swept volume ratio (>1.0) is not pronounced. The requirements in the environment of space place a number of constraints upon a Stirling engine/alternator design that are not present in terrestrial applications. High specific power is achieved by designing the engine for higher pressure and frequency operation than a terrestrial Stirling engine, and by using light weight materials where appropriate. Cylinder is the heart of the engine and it forms a major proportion of the total system mass. Mass and heat loss estimates and analysis have been carried out on the cylinder for various materials of construction. Based on the analysis feasibility exists for a Cu-Ni combination. The system would have a mass of 7kg with a specific power estimate of 0.28kW/kg and a conduction heat loss to mass ratio of 159W/kg. The system obtained by numerical analysis is modeled in system simulation software SIMULATIONX. The simulation of the system is studied and a sensitivity analysis performed in order to assess the parametric interdependency of the whole free piston Stirling engine system. The system sensitivity to piston and displacer mass is studied using the simulation model. Sensitivity results indicate that there is a range of mass values within which the system is operational, mass values outside the range makes the system non-functional. Also the range is a function of various parameters and detailed analysis is required in this direction in order to further optimize all the functional parameters. Engineering approximation is carried out using the curve fitting toolbox in MatLab to generate design equations in order to provide preliminary design data for the designer, further a scaling study is carried out at various power levels in order to assess the sensitivity of system geometry at various power levels.