The objective of this contribution is the consideration of structural and loading uncertainties in non-linear timedomain dynamic analyses of base excited buildings. Structural responses under strong seismic ground motion are of great interest in earthquake engineering. The enforced vibration is affected by non-linear and non-monotonic influences, e.g., plastic deformation or base excitation itself. In addition, these influences tend to a wide scatter of the results, which can not be neglected and complicate the design process. For simple structures, design spectra and safety coefficients take these uncertainties into account. To gain more precise insights, or for analyses of complex non-symmetrical buildings, simulations in time domain become necessary. A distinction is made between epistemic and aleatory uncertainties. Earthquake signals are generated synthetically as parameterized non-stationary random processes. Story stiffnesses and earthquake parameters are modeled as fuzzy numbers. Optimization regarding the computation time is performed taking advantage of the metamodel strategy.