We study experimentally the deformation and break-up of liquid-filled capsules trapped at an axisymmetric step constriction, and subjected to increasing pressure drops. We considered biological (trout fish eggs) and bioartificial (made of ovalbumin and alginate) ones, with the objective to characterize the transition to break-up. We find that both capsule populations behave as a brittle material. They do not exhibit any plastic deformation prior to break-up. Moreover critical pressure drop exhibits a stochastic behavior as known for the fracture of disordered media. The break-up probability follows a three-parameter Weibull distribution, from which one can deduce the capsule rupture characteristics.