Monte Carlo computer simulations are used to study the conformational free energy of a folded polymer confined to a long cylindrical tube. The polymer is modeled as a hard-sphere chain. Its conformational free energy F is measured as a function of lambda, the end-to-end distance of the polymer. In the case of a flexible linear polymer, PM is a linear function in the folded regime with a gradient that scales as f equivalent to vertical bar dF/d lambda vertical bar (ND-1.20 +/- 0.01)-D-0 for a tube of diameter D and a polymer of length N. This is close to the prediction f similar to (ND-1)-D-0 obtained from simple scaling arguments. The discrepancy is due in part to finite-size effects associated with the de Gennes blob model. A similar discrepancy was observed for the folding of a single arm of a three-arm star polymer. We also examine backfolding of a semiflexible polymer of persistence length P in the classic Odijk regime. In the overlap regime, the derivative scales f similar to N(0)D(-1.72 +/- 0.02)p-(0.35 +/- 0.01), which is close to the prediction f similar to (ND-5/3P-1/3)-D-0 obtained from a scaling, argument that treats interactions between deflection segments at the second virial level. In addition, the measured free energy cost of forming a hairpin turn is quantitatively consistent with a recent theoretical calculation. Finally, we examine the scaling of F(lambda) for a confined semiflexible chain in the presence of an S-loop composed of two hairpins. While the predicted scaling of the free energy gradient is the same as that for a single hairpin, we observe a scaling of f similar to D-1.91 +/- 0.03P-(0.36 +/- 0.01). Thus, the quantitative discrepancy between this measurement and the predicted, scaling is somewhat greater for S-loops than for single hairpins.