The shear behaviour of grouted joints has been studied in the recent past using the conventional direct shear apparatus, where the normal load on the joint plane is kept constant during testing. The Constant Normal Stiffness (CNS) condition is adopted in this study of shear behaviour of bolted joints, as the CNS condition represents a better approximation of the deformation behaviour of grouted joints in underground excavations as compared to the conventional Constant Normal Load (CNL) condition. A series of tests were conducted to study the behaviour of these stabilised joints under constant normal stiffness condition at an initial normal stress ranging from 0.13 MPa to 3.25 MPa, using a large scale CNS testing machine at a controlled strain rate of 0.5 mm/min. An analytical model has been developed to predict the shear resistance of bolted joints using the Fourier Series. The shear resistance of the bolted joint was defined as a function of the applied initial normal stress, the normal stiffness of the surrounding rock mass and the shear stiffness of the bolt. Fourier series was used to formulate the dilation behaviour during shearing, which in effect was utilized to predict the variation of normal stress during test process. Thus, using the analytical model, the complete stress profile for the bolted joint could be predicted at any normal stress and stiffness condition. The laboratory results were found to compare favourably with the predicted stress profiles from the model.