A concept called Allowable Load Set (ALS) is introduced and methods of finding its boundaries are developed. The resulting diagram allows an easy understanding of load and strength characteristics of a structure in relation to its integrity under uncertain loading conditions. The ALS is defined as the set of loads that are safe for a given structural or mechanical system. An allowable load diagram for an ALS visualizes the relation between a prescribed load and a degree of safety of the structure. Applications to multi-body mechanical systems are developed, with efficient algorithms of finding ALS for various postures. During the application of the algorithms, not only critical areas of the structure but also critical postures are identified.