The paper investigates the shape recovery behavior of a simple beam and a tape spring made of LDPE under prescribed deformation history at room temperature. The linear viscoelastic material properties of LDPE were measured via creep tests. An analysis of a LDPE beam under four-point bending with an imposed history of vertical deflection and reaction force was performed. A theoretical solution was constructed by employing the Alfrey's Correspondence Principle to the Euler-Bernoulli beam equation. The result was validated against a four-point bending experiment and a detailed nonlinear finite element simulation. Excellent agreement was obtained between theory, experiments and numerical simulations. A LDPE tape spring was fabricated and tested to provide an example of a simple deployable structure that recovers its deployed shape through a viscoelastic process for both equal sense and opposite sense folding.