The shear strength parameters of soil (cohesion and angle of internal friction) are quite essential in solving many civil engineering problems. In order to determine these parameters, laboratory tests are used. The main objective of this work is to evaluate the potential of Artificial Neural Network (ANN) and Regression Tree (CART) techniques for the indirect estimation of these parameters. Four different models, considering different combinations of 6 inputs, such as gravel %, sand %, silt %, clay %, dry density, and plasticity index, were investigated to evaluate the degree of their effects on the prediction of shear parameters. A performance evaluation was carried out using Correlation Coefficient and Root Mean Squared Error measures. It was observed that for the prediction of friction angle, the performance of both the techniques is about the same. However, for the prediction of cohesion, the ANN technique performs better than the CART technique. It was further observed that the model considering all of the 6 input soil parameters is the most appropriate model for the prediction of shear parameters. Also, connection weight and bias analyses of the best neural network (i.e., 6/2/2) were attempted using Connection Weight, Garson, and proposed Weight-bias approaches to characterize the influence of input variables on shear strength parameters. It was observed that the Connection Weight Approach provides the best overall methodology for accurately quantifying variable importance, and should be favored over the other approaches examined in this study.