Time-dependent strains in reinforced concrete (RC) members are usually estimated using approximate algebraic methods. This paper presents an exact method for estimating the time-dependent strains in RC members subjected to concentric axial compression, using creep compliance and shrinkage strain information for the corresponding plain concrete. The axial strain in concrete is taken to be the sum of shrinkage strain and the creep strain. Shrinkage strain in concrete is modeled as a: "lack-of-fit" problem. Assuming a linear viscoelastic constitutive law for concrete and a linear elastic constitutive relation for reinforcing steel, the corresponding one-dimensional viscoelastic boundary value problem is solved. It is assumed that there is a perfect bond between concrete and steel. The proposed method is validated using tests reported in the literature. The prediction of overall time-dependent axial strains under applied axial loads is found to match the observed test results closely. However, there are discrepancies in the relative magnitudes of creep and shrinkage strains, and the possible reasons for these are also discussed. © 2020 American Society of Civil Engineers.