Abstract: Flexible tensegrity structures can be used in a variety of engineering scenarios such as bridges building, robotic arms and probing robots. In the case of tensegrity robotic arms, a decrease in the cable prestress due to relaxation may bring about uncertainty in the actuated-deformation response, resulting in functional failure. Studying the propagation of uncertainty in cable relaxation in tensegrity structures is necessary for the quantitative control of robotic arm actuation displacements. However, tensegrity arms may contain tens or even hundreds of cables, and using the conventional Monte Carlo method would face a “dimension disaster”. By introducing a probabilistic model to the working time of the manipulator and combining with the independent identically distributed assumption, this paper includes the uncertainty of prestress relaxation into the clustered tensegrity structure reliability analysis. And a Polynomial Chaos Expansion (PCE) method with Least Angle Regression (LARS) is used to analyze the uncertainty propagation of the actuated displacement of a tensegrity arm, enabling fast prediction of the probability distribution of the structural response. For the 12-bar and 36-cabel tensegrity arm studied, the sparse PCE method can achieve accurate model prediction with only 500 finite element simulations as training data, which can solve the dimensionality problem and improve the analysis efficiency. Meanwhile, with the sparse PCE model, a sensitivity analysis of the design variables was carried out to quantify the cable influence on the arm’s movement. The result shows that the reliability of the tensegrity arm can be significantly improved by simply enhancing the most influential cable. The method presented can be applied to the uncertainty quantification of dynamics of tensegrity manipulators, and to the structural optimization with reliability constraints.