Ultrasonic metal welding (USMW) is one of the solid state joining techniques which provides an alternative approach of joining soft and highly conductive materials like aluminum and copper in an impeccable way. Expectancy of good joint strength is an inevitable step to monitor, control and optimize the process parameters in this welding technique. In the light of this, regression model, artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) are developed for predicting and simulating the joint strength for the USMW of Al-Cu sheets. The experiments are planned as per the full factorial design with three critical process parameters such as vibration amplitude, weld pressure and weld time to analyze tensile shear (TS) and T-peel (TP) failure loads. The analysis of variance (ANOVA) study explored that weld pressure has the most impact on the TS and TP followed by weld time and vibrational amplitude. Both of the artificial intelligence techniques were trained using the data attained from the experiment. Moreover, by comparing regression, ANN and ANFIS predicted results; ANFIS model provides less than 1% error and thus it can be considered as one of the reliable models to predict the weld strength in USMW process.