Over the past several decades, the use of composite materials has grown considerably. Typically, fiber reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature.In present work, a short review on linear viscoelasticity theory is performed to introduce the relation between linear elasticity and linear viscoelasticity theories. The safe load limit, a well defined parameter for columns made of linearly viscoelastic solid and fluid type materials with limited creep, is generalized to materially and geometrically linear viscoelastic structures in case of quasi-static and dynamic equations. To illustrate the concepts to be treated, a simple rigid bar spring/dashpot model simulating the behavior of imperfect columns is analyzed in detail. Next the imperfect column problem is formulated and solved. The results of the analysis of the creep deflection of the column showed that for fluid type materials the deflections increase continuously with time and become infinitely large only when the loading time is correspondingly large. However, large deflections are obtained in reasonably short periods of time if the applied load is near to the Euler load of the column. For solid type materials the deflections increase continuously with time and become infinitely large only when the load magnitude and loading time are correspondingly large. Various approximations in the solution technique are introduced which allow relatively simple procedures for the evaluation of the safe load limit. Finally a column is analyzed with a finite element code for which the results are compared, where possible, with closed form results, a comparison which shows satisfactory agreement.