Steel modular building structures are being increasingly adopted for a variety of building applications since their method of construction, despite being relatively new, offers many benefits over conventional constructional methods. Even though their behaviour under gravity (dead and live) loads is generally well understood, their response to lateral dynamic loads such as seismic and wind loads, is relatively less known. Due to their unique structural detailing, their structural response and failure patterns under lateral dynamic loading can vary considerably from that exhibited by conventional structures. Limited research has shown that under lateral loadings, modular structures tend to fail at the columns which are critical members whose failure can lead to partial or total collapse of the structure. This paper aims to mitigate this by shifting the failure away from the columns to inter-modular connections which can be allowed to deform in a ductile manner. Towards this end, this paper proposes two innovative inter-modular connections and investigates their performance under monotonic and cyclic lateral loading using comprehensive validated numerical techniques. The proposed connections have an additional steel plate and resilient layers to provide increased ductility and dissipation of seismic energy with desired ductile failure mechanisms. Three-dimensional numerical models of the proposed connections are developed in ABAQUS software considering geometric and material nonlinearities, as well as contact formulations to accurately capture their response to the lateral loads and failure propagations. The numerical model is verified based on experimental results in the literature and used for extensive parametric studies. Seismic reliance of the proposed connections in terms of ductility, failure patterns, and energy absorption are compared with those of a standard inter-modular connection currently used in modular buildings. The outcome of this study demonstrates that the proposed connections have superior dynamic performances compared to the standard inter-modular connections in use today. New information generated through this study will enable to improve life safety and dynamic performance of modular building structures under typical gravity loads as well as under seismic loading.