Abstract A concurrent explicit-implicit algorithm for time integration of the differential equations arising from a finite element discretization is described. The first step of the method consists of partitioning the finite element mesh into subdomains. As a consequence of this partition, the nodes in the resulting mesh form two distinct sets: interior nodes and interface nodes. Once these sets of nodes are identified, the method proceeds by integrating the interface nodes explicitly, and the interior nodes implicitly. Since the interior nodes in a specific subdomain are not shared by any other subdomain, they can be integrated independently. As a direct consequence, concurrency is introduced. Thus, this method is very well suited for implementation in parallel computers. In addition to this feature, the concurrent explicit-implicit algorithm is also expected to speed up computations, even on a sequential computer, by reducing the equation solving effort. Some considerations on the conversion of an originally sequential finite element analysis program to implement this method is given. Numerical examples are presented to illustrate the method.