Creep of concrete could cause adverse stress redistributions and excessive deformations. Its structural effects can be assessed by conducting time-step analysis using finite-element methods with time-integration formulation, in which the creep strain at any time is determined as the cumulative creep responses to stress increments in previous time steps. This process entails memorisation of the stress histories of all the concrete elements, leading to prohibitive demands of computer memory and time, especially for large and complex structures. To avoid having to memorise the stress histories, a remnant creep based visco-elastic model is developed, whereby the remnant creep strains are employed to evaluate the incremental creep strains. This model circumvents the need for memorising the stress histories and possesses a great flexibility in fitting with codified creep formulas. Numerical examples are presented to demonstrate the general applicability of the proposed model.