The vulnerability of process plants to natural hazards has been demonstrated in the last decades by a number of catastrophic events. Unfortunately, despite the continuous evolution of the knowledge on this matter, there is a lack of widely accepted and standardized procedures to perform a risk assessment of process plants subjected to Na-Tech hazards. In this paper, a new tool for the probabilistic seismic risk assessment of process plants is thus proposed, based on Monte Carlo simulations. Starting from the seismic hazard curve of the site in which the plant is placed, a multi -level approach is proposed. In this approach, the first level is represented by the components seismically damaged, whereas the following levels are treated through a classical consequence analysis, including propagation of multiple simultaneous and interacting chains of accidents. This latter is applied through the definition, for all relevant equipment, of proper correspondences between structural damage (i.e., damage states) and loss of containment events. The procedure has been implemented in the software "PRIAMUS" (Probabilistic Risk Assessment with Monte Carlo simulations of Process Plants Under Seismic Loading). By automatically generating samples of damage propagation chains, the risk of the plant can be easily quantified in terms of economic losses, content losses, damage propagations or final damage scenarios. The application to a petrochemical plant shows the potentiality of the method and envisages possible further evolutions.