The evaluation of seabed response under wave loading is important for prediction of stability of foundations of offshore structures. In this study, a stochastic finite element model which integrates the Karhunen-Loève expansion random field simulation and finite element modeling of wave-induced seabed response is established. The wave-induced oscillatory response in a spatially random heterogeneous porous seabed considering cross-correlated multiple soil properties is investigated. The effects of multiple spatial random soil properties, correlation length and the trend function (the relation of the mean value versus depth) on oscillatory pore water pressure and momentary liquefaction are discussed. The stochastic analyses show that the uncertainty bounds of oscillatory pore water pressure are wider for the case with multiple spatially random soil properties compared with those with the single random soil property. The mean pore water pressure of the stochastic analysis is greater than the one obtained by the deterministic analysis. Therefore, the average momentary liquefaction zone in the stochastic analysis is shallower than the deterministic one. The median of momentary liquefaction depth generally decreases with the increase of vertical correlation length. When the slope of the trend function increases, the uncertainty of pore water pressure is greatly reduced at deeper depth of the seabed. Without considering the trend of soil properties, the wave-induced momentary liquefaction potential may be underestimated.