Cracks usually propagate dynamically that makes them so dangerous. However, most crack simulations are based on quasi-static analyses because they are simpler than the dynamic ones. Is it correct to use quasi-static analyses instead of the dynamic ones? Will the quasi-static and dynamic simulations provide similar results? We try to answer these questions in the present work. We compare results of quasi-static and dynamic simulations of crack propagation in aneurysm material. We use the material-sink (MS) approach, which is based on the notion of the diffused bond breakage. The latter feature implies a local loss of material and, consequently, decrease of mass density, which, in its turn, means that both stiffness and inertia go down in the damaged zone. The cancellation of inertia is an important feature of the MS approach in contrast to more formal regularization theories as phase field, gradient damage, and other nonlocal formulations. The MS approach is implemented within commercial finite-element software abaqus. A reduced mixed finite-element formulation is adopted to circumvent the volumetric locking and an implicit staggered solution algorithm is developed via the user-defined element subroutine . Considered examples show that the onset of crack instability under static loads is followed by the dynamic rather than quasi-static crack propagation. Moreover, dynamic and quasi-static simulations, generally, provide different results.