To conduct a sensitivity analysis of the relevant parameters that impact the mechanics of tunnel construction in karst areas, firstly, the orthogonal design and range analysis method is applied to sort the 11 kinds of karst-tunnel-influencing factors from high to low according to the sensitivity degree. Secondly, the random forest algorithm based on an orthogonal experimental design is applied to the feature importance ranking of the influencing factors of karst tunnels. Thirdly, according to the results of the sensitivity analysis, the optimum combinations of influencing factors of tunnel construction in karst areas is obtained. The research based on these two methods shows that when taking the vertical displacement as the target variable, the parameters with the highest feature importance are A6 (tunnel diameter) and A10 (tunnel buried depth). When taking the first principal stress as the target variable, the most important influencing factors are A10 (tunnel buried depth) and A9 (location of karst cave). When taking the principal stress difference as the target variable, the most important influencing factors are A10 (tunnel buried depth) and A6 (tunnel diameter). The level combination of the 11 influencing factors obtained by taking the principal stress difference as the target variable was more balanced than the vertical displacement and the principal stress difference as the target variables. The results of this study will provide a theoretical basis to study key parameters in the response of mechanical characteristics to the safe construction of tunnels in karst areas.