This thesis describes the development of a methodology for the development of interactive, numerical software (INS) and then assesses its effectiveness via the development of a finite element package, INFESA. The uniqueness of this package which is designed to run on small minicomputers, lies in its portability and versatility and thus makes an original contribution to finite element software and applications. The thesis begins by setting the scene of software development and especially software development methodology. Within this context, the objectives of the research are then clearly defined. Chapter two defines the precise meaning of the term 'Interactive, Numerical Software' and describes in detail the authors previous experience in producing such software for use in an educational environment. A critical view of INS I as applied to finite element software is presented in chapter three and this, together with the lessons learnt from chapter two, combines to determine the design strategy for INFESA. The fourth chapter summarises the mathematical and numerical techniques in INFESA. An important part of INFESA C%M the mesh generation routines and the pate. presented in chapter. Live after a detailed survey of the historical developwent of mesh generation techniques. INFESA is critically assessed with respect to its developmental objectives in chapter seven. This chapter also includes the description and successful resolution of an original problem initiated by British Steel whose unusual and highly non-linear boundary conditions provide a difficult task for any existing finite element software. The solution of this problem provides a demonstration of the versatility of INFESA. The final chapter consists of concluding remarks and some suggestions for the further development of the system.