The paper introduces the method of the modal reduction of systems that experience the Coriolis acceleration or gyroscopic effect component. In such cases corresponding system equations are non-self-adjoined. To solve the problem modal reduced model is built up for the system without Coriolis acceleration or gyroscopic effect terms. These phenomena are next included by application of any lumping technique. Hence, the final reduced model is a hybrid one, obtained by both lumping and modal methods of modelling.