Computer models can describe complicated phenomena encountered in science and engineering fields. To use these models for scientific investigation, however, their generally long running times and mostly deterministic nature require a specially designed experiment. This paper presents a class of Latin hypercube designs developed from the rotation of factorial designs. These rotated factorial designs are easy to construct and preserve many of the attractive properties of standard factorial designs: they have equally-spaced projections to univariate dimensions and uncorrelated regression effect estimates (orthogonality). A thorough application of the newly proposed design in mechanical engineering is presented. New results on the rotated mixed-level factorial designs are discussed.