The article studies the inelastic seismic response assessment of structures with spatially varying material properties via the stochastic finite element method. This is a problem with a complex response function due to stochastic variability and material nonlinearity. Existing formulations either assume linear-elastic behaviour, or use dense models in order to capture both stochasticity and inelasticity. This results to models that require excessive computational resources. The article shows that for material nonlinear problems, the stochastic variability can be taken into consideration using flexibility-based models which allow performing repeated time-history simulations within a reasonable computational time, without loss of accuracy. The interpolation can be adjusted through a user-defined parameter, thus avoiding the need for a dense FE mesh. Contrary to past research, the modelling proposed has many applications in structural engineering, since it allows nonlinear, static or dynamic, simulations of real-scale frame structures with stochastic properties. The proposed method is demonstrated in the framework of the spectral representation method combined with Monte Carlo simulations, but it can be combined with any other method for the description of the stochastic field. A generic single-storey steel frame and a six-storey reinforced concrete frame are considered in order to demonstrate the efficiency of the proposed modelling.