We show how you can carry out systematic sensitivity analysis (SSA) with respect to parameters and/or shocks, which vary according to a specified covariance matrix. You can use the existing SSA tools in RunGTAP or RunGEM to do this if your model is implemented in GEMPACK. Those SSA tools assume that all parameters or shocks are varying independently (i.e., the distributions of all parameters or shocks are uncorrelated) or together (i.e., are completely correlated). The techniques in this paper remove those restrictions. However, users need to make small modifications to the TAB file for the model. Different modifications are needed for different SSA scenarios. Further, the standard SSA procedure built into RunGTAP and RunGEM allows you to compute the sensitivity of model results either with respect to variations in parameter values or with respect to variations in shock values, but you cannot vary both parameters and shocks at the same time. Our discussion concentrates on the parameter case. However, we later show how shock variation may be modelled as a type of parameter variation. This opens the door to simultaneous variation of shocks and parameters. We include worked examples of the techniques described, based on the standard GTAP Model.