Dynamic building energy simulation and life cycle assessment (LCA) are useful ecodesign tools to mitigate the energy and environmental impacts of buildings. Various uncertain factors can affect the building energy and environmental modelling, including continuous and categorical factors (i.e., discrete factors without logical ranking). Sensitivity analysis (SA) is applied to identify the most influential factors on which additional research efforts are needed to increase the robustness of results. The Sobol method (Sobol) is the reference SA method, but it requires a significant amount of computation. Less time-consuming methods, such as an adaptation of the Morris screening (Morris), have shown a good ability to quantify the influence of factors, but their performance has not been investigated for categorical factors having many (more than two) levels. Two strategies (2LA-Morris and MA-Morris) based on the adaptation of Morris are proposed to handle many-level factors. Their performance is compared to that of Sobol based on four criteria: computation time, factor's relative influence, factor's ranking, and ability to detect interactions. For the LCA of a house including 24 uncertain factors, MA-Morris was able to quantify the influence of factors in the same way as Sobol, while reducing the computation time by a factor of 12.