Energy storage systems (ESSs) are acknowledged to be a promising option to cope with issues in high penetration of renewable energy and guarantee a highly reliable power supply. In this paper, a two-step optimal allocation model is proposed to obtain the optimal allocation (location and size) of stationary ESSs (SESSs) and mobile ESSs (MESSs) in the resilient distribution networks (DNs). In the first step, a mixed-integer linear programming (MILP) problem is formulated to obtain the preselected location of ESSs with consideration of different scenarios under normal operation conditions. In the second step, a two-stage robust optimization model is established to get the optimal allocation results of ESSs under failure operation conditions which are solved by column-and-constraint generation (C&CG) algorithm. A hybrid ESS allocation strategy based on the subjective and objective weight analysis is proposed to give the final allocation scheme of SESSs and MESSs. Finally, the proposed two-step optimal allocation model is demonstrated on a modified IEEE 33-bus system to show its effectiveness and merits.