Un-trenched submarine pipelines will experience the wave and current loads during their design lifetime which potentially tend to destabilize the pipeline both horizontally and vertically. These forces are resisted by the interaction of the pipe with the surrounding soil. Due to the uncertainties involved in wave, current and soil conditions, there will be a complex interaction between wave/current, pipeline and seabed that needs to be properly accounted for. The design of submarine pipelines against excessive displacement due to hydrodynamic loads (DNV-RP-F109) is defined as a Serviceability Limit State (SLS) with the target safety levels as given in DNV-OS-F101 (2013). In this paper uncertainties associated with on-bottom stability design of submarine pipelines are investigated. Monte Carlo Simulations (MCS) are performed as the basis for probabilistic assessment of the lateral stability of the pipeline located on the seabed. Application of the method is illustrated through case studies varying several design parameters to illustrate the importance of each design parameter for exceeding a given threshold of the SLS criterion. Uncertainties in significant wave height and spectral peak period are found to be important parameters in describing the UR distribution. Type of soil has also an impact on the distribution of UR, i.e. how the passive resistance in the pipe-soil interaction model is accounted for. Therefore, the definition of characteristic values of both loads and resistance variables are important for the Utilisation Ratio (UR).