This paper presents the displacement, stress and reliability analysis of structures with a mixture of random and interval parameters under uncertain static loads. The structural displacement and stress responses are random interval variables when some structural parameters/loads are modelled as random variables and others are considered as intervals. The random interval perturbation method and random interval moment method are employed to predict the random interval structural response. The structural reliability is not a deterministic value but an interval as the structural responses are random interval variables. The expressions for lower and upper bounds of reliability index, probability of failure and reliability of structural elements and systems are then developed by using the combination of the structural reliability theory and interval approach. Truss and frame structures are used as examples to demonstrate the validity and feasibility of the presented methods. The probabilistic and interval characteristics of structural static response and reliability are investigated and some useful conclusions are given.