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This thesis describes an experimental and theoretical investigation of the stresses and deformations in a square-based pyramidal-sheet roof. Four perspex pyramids were tested, and one beam of five perspex pyramids and one of seven pyramids. A larger steel model of seven pyramids was also tested to give a better idea of the behaviour of the thin metal structure. Single pyramids were loaded at the apex, and strains and deflections measured when the base was fixed and simply-supported. Deflection measurements were taken with perspex trusses. The stress distributions in a pyramid of the steel truss and its base plate were obtained from strain measurements; the position of this pyramid in the span being varied. Deflect-ions of the truss were also measured. The theoretical work was divided into three parts, (i) an approximate method was used to calculate the deformations of single pyramids and trusses. In this method, an equivalent skeletal system was used to replace the actual structure. (ii) the stress distributions in a single pyramid having its base simply-supported and fixed and subjected to a vertical load at its apex were calculated. In both cases, the walls were considered as plane stress problems having certain assumed boundary conditions. (iii) an approximate method for calculating the buckling load limits of a pyramid was suggested. The pyramid wall was treated as a trapezoidal plate uniformly compressed along its two parallel edges. The calculated deflections for the five exploratory models and the steel truss compared well with measured values. The theoretical stress distributions in the simply-supported pyramid were close to the experimental distributions but were lees accurate in the fixed pyramid. The buckling load calculated for a pinned trapezoidal plate compared well with that obtained from test on one of the exploratory models.