Multidimensional effects through porous building elements is barely explored in the literature due to many difficulties such as modeling complexity, computer run time, numerical convergence and highly moisture-dependent properties. Furthermore, when the multidimensional effect is considered, thermal bridges may play an important role on the hygrothermal building performance due to local increase of heat and mass flux densities. Therefore, in order to analyze the effects of building lower and upper corners, a multidimensional model has been developed to calculate the coupled heat, air and moisture transfer through building envelopes. For improving the discretized model numerical stability, the algebraic equations are simultaneously solved for the three driving potentials: temperature, vapor pressure and gas pressure gradients. In the results section, the coupling of the upper corner, wall, lower corner, ground and floor are analyzed for different boundary conditions in terms of temperature and relative humidity profiles, vapor flow and heat flux, showing the importance of a detailed hygrothermal analysis for accurately predicting building energy consumption, thermal comfort and mould growth risk.