In this study, we developed Different Artificial Intelligence (AI) models namely Artificial Neural Network (ANN), Adaptive Network based Fuzzy Inference System (ANFIS) and Support Vector Machine (SVM) for the prediction of Compression Coefficient of soil (Cc) which is one of the most important geotechnical parameters. A Monte Carlo approach was used for the sensitivity analysis of the AI models and input parameters. For the construction and validation of the models, 189 soft clayey soil samples were analyzed. In the models study, 13 input parameters: depth of sample, bulk density, plasticity index, moisture content, clay content, specific gravity, void ratio, liquid limit, dry density, porosity, plastic limit, degree of saturation, and liquidity index were used to obtain one output parameter "Cc". Validation of the models was done using statistical methods such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of determination (R2). Results of the model validation indicate that though performance of all the three models is good but SVM model is the best in the prediction of Cc. The Monte Carlo method based sensitivity analysis results show that out of the 13 input parameters considered for the models study, four parameters namely clay, degree of saturation, specific gravity and depth of sample are the most relevant in the prediction of Cc, and other parameters (bulk density, dry density, void ratio and porosity) are the most insignificant parameters for the prediction of Cc. Removal of these insignificant parameters helped to reduce the dimension of the input space and also model running time, and improved significantly the performance of the AI models. The results of this study might help in selecting the suitable AI models and input parameters for better and quick prediction of the Cc of soil.