This paper presents a new framework for analysis of structures subjected to imprecise or uncertain displacements through application of interval methods. This pertains to quantification of uncertainty existing in the induced displacements using unknown-but-bounded or interval variables. In deterministic conventional displacement-based structural methods, the unknown displacements are obtained followed by determination of internal forces. In order to attain sharp results, using this method, the two main steps of conventional static analysis is combined which leads to determination of bounds of internal forces/moments as well as internal stresses directly. Using this method, the functional dependencies of uncertain interval parameters are considered in the calculations leading to obtaining sharp results. An example illustrating the behavior of the method developed is presented and the results are compared with Monte-Carlo simulations results.