The lessons learnt from recent strong seismic events have demonstrated that severe physical damages to port facilities are not related only to the ground shaking but also to the ground shaking induced soil liquefaction of loose, saturated soils that often prevail at coastal areas. Although progress has been made on the influence of ground shaking and liquefaction on the structural response of buildings, studies coupling both phenomena are very limited. To bridge this gap, the objective of this study is the proposal of an analytical methodology for the vulnerability and risk assessment of typical port low-code (LC) reinforced concrete (RC) moment resisting frame (MRF) buildings due to combined ground shaking and liquefaction, using reliable methods and techniques. The direct one-step approach where the soil and the structure are modelled and analysed as a single system is used considering significant soil nonlinearity induced by soil liquefaction. We perform rigorous two-dimensional (2D) nonlinear incremental dynamic analysis (IDA) of the soil-structure systems using OpenSees. Coupled bivariate fragility surfaces are derived due to the combined effect of ground shaking and liquefaction considering the soil-structure interaction (SSI). Finally, we assess risk in terms of economic losses (repair cost to replacement cost) due to the combined effect of ground shaking and liquefaction for the RC frame buildings of Thessaloniki port. Through this application the applicability and effectiveness of the proposed methodological framework and the respective fragility surfaces is verified.