The mechanical response of rock bridges plays a key role in the stability of concrete and rock structures. In particular, the tensile failure of non-persistent discontinuities can result in their coalescence and the failure of rock or concrete engineering structures. The effect of non-persistent joint parameters on rock structures' failure under tensile mode has not been investigated by many researchers yet. Many non-persistent jointed Brazilian concrete discs are tested under diametral loading in this work, to study the influence of joint spacing, joint continuity factor, loading direction with regard to joint angle, and bridge angle on their tensile behavior. Heuristic methods like artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS) and a combination of ANFIS with particle swarm optimization (ANN-PSO) and genetic algorithm (ANFIS-GA) were adopted to explore the relationship between tensile strength and stiffness as the response and non-persistent joint parameters as input parameters. The results revealed that all the applied intelligent methods have the ability to predict tensile strength of non-persistent jointed discs, and their outputs are consistent with laboratory results; however, the ANN approach had the best performance with R2 = 0.966, RMSE = 0.176. In addition, parametric analysis of the proposed model showed that the model is highly sensitive to joint continuity factor and loading direction, while it is sensitive to joint spacing and bridge angle.