Abstract Eigenfrequency loci veering, which indicates strong mode coupling and sometimes mode localization, is a much sought-after property in the applications of mass sensing and opto/electromechanics. A weak physical coupling is the mechanism responsible for the eigenfrequency loci veering and overhang is a widely used structure to realize such mechanism. A continuum model, which is more accurate and straightforward as compared with the discrete models, is presented for the structure of two overhanged cantilevers. The eigenvalue problem formulation based on this continuum model leads to a direct computation of the eigenfrequencies, which does not involve any numerical discretization procedure. A comprehensive study on the eigenfrequency loci veerings and mode splittings of the overhanged structure is presented. The influences of various parameters on the eigenfrequency loci crossing and veerings are also systematically studied. An efficient optimum design tool for the eigenfrequency loci veering of an overhanged structure is provided by the continuum model together with a direct computation method.