Drop coalescence in viscoplastic materials is present in various industrial applications and the environment. The plasticity of the surrounding material affects drop rise, collision, and film drainage dynamics, and knowledge about these is essential for designing and operating industrial mixer and separator units. Despite its importance, the coalescence of drops in yield stress materials is not entirely understood. In this work, we investigate the effects of the surrounding material plasticity on the rise and interfacial coalescence initiation of Newtonian drops using direct numerical simulations. Plastic effects contribute to the formation of smaller and spherical films, which facilitate the film drainage process on the one hand, but also to an increase in the resistance of the film to flow, which makes the drainage process more difficult on the other hand. The fluids’ interfaces are less deformable for high surface tension regimes, and the flow resistance effects become more significant than the film shape change effects. As a result, the drainage time tends to increase with the level of plasticity. For low surface tension regimes, the fluid interface is more deformable, and film drainage time tends to decrease with an increase in the level of plasticity.