Due to its iterative nature, engineering design typically involves the analysis of several design candidates before a final design decision can be made. Since the number of design candidates that can be considered is often limited by the availability of computational resources, design reanalysis methods have been proposed in order to extend those resources. These methods attempt to reduce the cost of a design reanalysis by utilizing information derived from a previous analysis. In the past these methods have had only limited success since they have been able to cope only with relatively small design changes. In this paper an application of rational approximation theory is made which overcomes this problem. The basic approach is to treat the design change as a numerical homotopy problem and apply a rational approximation method to evaluate the solution. In order to guarantee robustness a new rational approximation method is used which has improved numerical properties.