This paper presents a three-dimensional finite-deformation cohesive element and a class of irreversible cohesive laws for simulating dynamic crack propagation. The cohesive element governs the separation of crack flanks according to an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with conventional finite element discretization of the bulk material. The method is demonstrated through the simulation of a drop-weight dynamic fracture test, showing its predictive ability. The ability of the method to approximate the experimentally observed crack-tip trajectory is particularly noteworthy. The paper develops a finite-deformation irreversible cohesive law, which accounts for the irreversibility of decohesion processes. The cohesive law is derived from thermodynamic principles and is expressed in terms of a free energy function. The cohesive law is then implemented in a finite element framework, where the cohesive surface is represented by two surface elements that coincide in the reference configuration. The cohesive elements are compatible with general bulk finite element discretizations and can be used to bridge pairs of tetrahedral elements. The cohesive law is implemented as a mixed boundary condition, relating tractions to displacements at boundaries or interfaces. The cohesive elements are surface-like and are compatible with general bulk finite element discretizations of the solid, including those which account for plasticity and large deformations. The cohesive elements bridge nascent surfaces and govern their separation in accordance with a cohesive law. The simulation of the drop-weight dynamic fracture test demonstrates the method's ability to track dynamically growing three-dimensional cracks in a solid undergoing finite deformations. The calculations show that the method can accurately simulate the crack growth process, including the emergence of the crack through the upper surface of the specimen. The crack front develops a small curvature as it propagates and lags behind somewhat near the free surface due to enhanced plastic activity in that region. The numerical simulation captures some of the salient features of the experimental record, such as the initial acceleration of the crack tip, the subsequent oscillations about a plateau, and the final drop in velocity as the crack joins up with the top surface of the specimen. The method is shown to be effective in simulating dynamic crack propagation in three-dimensional solids. The cohesive elements are endowed with full finite kinematics and are capable of accurately tracking the evolution of cracks under large deformations. The method is particularly useful for simulating brittle fracture in materials such as C-300 steel. The results demonstrate the versatility and predictive ability of the method in simulating dynamic crack propagation in three-dimensional solids.This paper presents a three-dimensional finite-deformation cohesive element and a class of irreversible cohesive laws for simulating dynamic crack propagation. The cohesive element governs the separation of crack flanks according to an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with conventional finite element discretization of the bulk material. The method is demonstrated through the simulation of a drop-weight dynamic fracture test, showing its predictive ability. The ability of the method to approximate the experimentally observed crack-tip trajectory is particularly noteworthy. The paper develops a finite-deformation irreversible cohesive law, which accounts for the irreversibility of decohesion processes. The cohesive law is derived from thermodynamic principles and is expressed in terms of a free energy function. The cohesive law is then implemented in a finite element framework, where the cohesive surface is represented by two surface elements that coincide in the reference configuration. The cohesive elements are compatible with general bulk finite element discretizations and can be used to bridge pairs of tetrahedral elements. The cohesive law is implemented as a mixed boundary condition, relating tractions to displacements at boundaries or interfaces. The cohesive elements are surface-like and are compatible with general bulk finite element discretizations of the solid, including those which account for plasticity and large deformations. The cohesive elements bridge nascent surfaces and govern their separation in accordance with a cohesive law. The simulation of the drop-weight dynamic fracture test demonstrates the method's ability to track dynamically growing three-dimensional cracks in a solid undergoing finite deformations. The calculations show that the method can accurately simulate the crack growth process, including the emergence of the crack through the upper surface of the specimen. The crack front develops a small curvature as it propagates and lags behind somewhat near the free surface due to enhanced plastic activity in that region. The numerical simulation captures some of the salient features of the experimental record, such as the initial acceleration of the crack tip, the subsequent oscillations about a plateau, and the final drop in velocity as the crack joins up with the top surface of the specimen. The method is shown to be effective in simulating dynamic crack propagation in three-dimensional solids. The cohesive elements are endowed with full finite kinematics and are capable of accurately tracking the evolution of cracks under large deformations. The method is particularly useful for simulating brittle fracture in materials such as C-300 steel. The results demonstrate the versatility and predictive ability of the method in simulating dynamic crack propagation in three-dimensional solids.