In this paper, a study is made of the influences of orthotropic properties and boundary conditions on the free vibrations of a rotating, truncated, circular orthotropic conical shell. The study includes the effects of the Coriolis and centrifugal accelerations and the initial hoop tension. It is based on the Love first-approximation theory and Galerkin procedure, Results are obtained for the frequency characteristics of different orthotropic parameters, rotating velocities, cone angles and boundary conditions. Influences of orthotropic properties and boundary conditions on the relationships between frequency parameter and rotation velocity are discussed for different cone angles. To validate the present analysis, comparisons are made with those available in the open literature and very good agreements are obtained. (C) 2000 Elsevier Science Ltd. All rights reserved.