The paper presents a method which enables us to perform creep analysis of RC elements with uncracked cross-sections relying on the evaluation of an average stress strain state in a sense to fulfill Volterra's integral term in time interval elapsed after loading and the prediction of an actual state at the time considered. The analytically derived expressions for time-dependent stresses, strains and curvatures are very simple, being gained by a newly proposed relation for the ageing coefficient, constitutive law for creep and the classical formulae of strength of materials. The method proposed is mathematically tractable, as well as accounting for the variation of elastic modulus. A validity of the method proposed was proven by direct calculation of the time-dependent parameters in the analysis of various RC elements. The approach gives exact values of the time-dependent stress strain state as those determined using the age-adjusted effective modulus method involving a sophisticated relaxation procedure. The method does not require the introduction of the fictitious restraining actions dramatically simplifying computation and could be used as a simple alternative approach for the exact analysis of RC uncracked elements. Numerical examples and methodology for applicability to RC structures/elements were also developed.