Ettringite and thaumasite are the main byproducts of complex chemical reactions that take place in cementitious materials during sulfate attack. These two sulfate-bearing crystals are known to experience excessive strains in various crystallographic directions during precipitation. Considering that this process can cause significant structural damage to the hardened cement paste, the current study investigates the effects of strain intensity and direction by simulating the atomic structures of ettringite and thaumasite subjected to a range of uniaxial and biaxial strains. For this purpose, reactive molecular dynamics simulations are performed to understand how the main chemical bonds respond to external strains. This sheds light on the atomistic processes underlying the plastic behavior of ettringite and thaumasite under different straining conditions. From biaxial simulations, the flow stresses are determined, particularly to characterize the plane stress flow surfaces of ettringite and thaumasite. A set of failure criteria are then examined to identify the criterion that properly captures the intrinsic features observed in the response of ettringite and thaumasite. The outcome of this study contributes to developing representative constitutive models that can be further employed to evaluate and optimize the mechanical properties of cementitious materials exposed to sulfate-rich environments.