Formulation and algorithmic treatment of a rate-dependent plastic–damage model modified to capture large tensile cracking in cyclic-loaded concrete structures are presented in detail for a three-dimensional implementation. The plastic–damage model proposed by Lee and Fenves in 1998 was founded based on isotropic damaged elasticity in combination with isotropic multi-hardening plasticity to simulate cracking and crushing of concrete under cyclic or dynamic loadings. In order that the model can capture large crack opening displacements, which are inevitable in plain concrete structures, the excessive increase in plastic strain causing unrealistic results in cyclic behaviors is prevented when the tensile plastic–damage variable controlling the evolution of tensile damage is larger than a critical value. In such a condition, the crack opening/closing mechanism becomes similar to discrete cracking. The consistent tangent operator required to accelerate convergence rate is also formulated for the large cracking state including viscoplasticity. The validation and performance of the modified algorithm implemented in a special finite element program is exemplified through several single-element tests as well as three structural applications. The last example examines the model in the seismic fracture analysis of Koyna dam as a benchmark problem and the resulting crack profile is compared with the available experiment. The numerical experimentations well demonstrate that the developed model whose modification is necessary to properly simulate the cyclic behavior of plain concrete subjected to large tensile strains is robust and reasonably accurate. Copyright © 2012 John Wiley & Sons, Ltd.