Fibre-matrix composites which have both light-weight and high strength properties have recently been receiving considerable attention as possible materials for structural applications in the Civil Engineering industry. One area of difficulty in the utilisation of these materials is the jointing of one component to another. The technology of adhesive bonding, already well established in the aerospace industry, offers a possible solution. The single and double lap joints and the tubular lap joint using the crimped and bonded technique represent the simplest jointing configurations. These are, therefore, the most likely to find practical applications in the Civil Engineering field. The present study has concentrated on the stress analysis of these three configurations, which will be defined hereafter as the 'Primary Configurations.' Two analytical techniques for the investigation of the primary configurations will be presented; the first uses a classical mathematical approach whereas the second uses the computer-based numerical finite element method. In both techniques, the analyses were extended to permit nonlinear adhesive yielding and this enabled an ultimate load capacity to be predicted. The classical analytical technique is an attempt to develop practical methods for a solution of the linear and nonlinear problem, as opposed to the more rigorous, but costly, finite element theory. An assessment was made of the validity of the two analytical techniques by comparing case studies for the primary configurations. In the case of the nonlinear classical theory, theoretical failure envelopes were compared with a series of experimental joint failures. To permit this work to be undertaken, some typical structural epoxide resin adhesives were tested in order to obtain their elastic and yielding characteristics. Manufacturers rarely quote detailed mechanical data for their products in the literature and it is anticipated that this work will be of interest to other investigators of adhesive bonded joints. The classical and finite element analytical techniques have been verified by the use of case studies. From a comparison with experimental studies the nonlinear classical method has been shown to be capable of predicting ultimate load for the double and tubular lap configurations. For the single lap configuration the analysis can only approximate the failure load. An experimental and an analytical investigation of the crimped and bonded joint has provided an understanding of the parameters that influence failure of this joint. This has led to a modified end grip which gives an improved transfer of stress to the tubular section and has an improved load bearing capacity.