When designing a building, the most of the important component is the roof. The selection of roofs for building depends on factors like type of building, type of foundation, roofing materials, roof loads, the climate, economy, the availability of materials, and the ease of construction. This study is focused on gable roof structures with two different supported structures of the ridge beam which are known as simply supported ridge beam structure and fixed supported ridge beam structure. The simply supported structure can be defined as the ends of the ridge beam are formed to stand freely on supports and the fixed supported structure can be defined as the ends of the ridge beam are supported to restrain against rotation and vertical movement. The study is considered jack wood beams which have the same length as 198 inches (5.03m) but have different cross-sectional area; 2x4inch2, 2x5inch2, 2x6inch2, 3x4inch2, 3x5inch2 and 3x6inch2. Further 11 Jack wood rafters which have the length 144 inches (3.66m) and cross sectional surface area 2x3 inch2 are used. Two Jack wood king post trusses that have kingposts with the length 30 inches (0.7m) are used for fixed supported structure to fix the beam between two supporters. The roof pitch angle is approximately 300. According to general fact, the deflection value of simply supported beam is higher than the deflection value of fixed supported beam. In this study, an attempt will be made to investigate the deformation of the ridge beam when it is simply supported and fixed supported and from that observe the optimum supported structure that can be used to design a roof of a building more constructive manner. Moreover by using the results, the validity of the general fact can be also proved. The major mathematical part in this study is to generate the model to calculate deflection of the ridge beam when it is simply and fixed supported by using Euler-Bernoulli Beam theory and Fourier series. The results showed that the deflection value of simply supported beam around 0.8-0.04 m and thedeflection value of fixed supported beam around 0.008-0.001 m. According to results, the study was confirmed the general fact of the deflection values of simply supported beam structure has higher than fixed supported beam structure.