Electric power distribution systems are generally more prone to disruption from natural hazards than transmission systems due to their often less redundant circuit structures. However, seismic risk analysis for distribution systems is rare compared to the rich body of literature focusing on transmission systems. This paper proposes a seismic risk assessment framework for electric power distribution systems considering both the network topology and the functional vulnerability of distribution substations. Implicit Z-bus method is applied to solve distribution system power flow and evaluate system serviceability. Monte Carlo simulation is applied to obtain probabilities of the scale of unserved loads resulting from disconnection and abnormal voltage condition. The seismic risk is jointly quantified using multiple risk metrics, and importance measures are used to determine criticality of substation components for prioritisation of seismic retrofit. The seismic risk assessment framework is applied to the CIGRE medium voltage distribution test network and two ground motion intensity scenarios – one for peak ground acceleration values based on a scenario earthquake and the other for uniformly distributed peak ground acceleration across the network. The framework allows the quantification of different network topologies and substation configurations. This enables network owners and operators to evaluate the seismic vulnerability of their substation configuration and network topology, identify potential bottlenecks of the systems and thus inform effective planning and risk-reduction investments.