Tensegrity systems typically contain a large number of members, and possess a high degree of statically indeterminacy. However, a number of members are critical to system integrity and serious strength reductions can be produced by loss of any of them. Furthermore, when these members are lost suddenly, their forces are shed in a dynamic manner into the structure, causing more severe damage. This paper presents a numerical study on the sensitivity of tensegrity systems to both gradual and sudden member losses, taking into account both geometric and material nonlinearities. Also, other parameters, considered in this work, include the self-stress level, slenderness ratios of struts and damping ratios. The conclusions, drawn from this study, can in turn, lead to the suggestion of some guidelines for the design of such systems.