Herein we show a density functional theory‐based study performed on two recently predicted polymorphs of the BeH2 monolayer, α‐BeH2 and β‐BeH2. The α‐BeH2 phase possesses an in‐plane negative Poisson's ratio (NPR), introducing it into the unique group of auxetic materials. Our assessment delves into the linear‐elastic and finite‐strain regimes to understand both polymorphs' structural and mechanical responses to deformation. We find that the in‐plane NPR is shown to be only parallel to the bonds in α‐BeH2 and remains along the uniaxial tensile path. Concomitantly, an out‐of‐plane transition toward auxetic is also revealed in regions exhibiting conventional Poisson's ratios, making α‐BeH2 a bidirectionally auxetic material. While phase transitions in β‐BeH2 are triggered at very short strains, α‐BeH2 displays excellent elasticity against tension, superior to that of most currently known 2D materials.