Abstract This paper extends the previous applications of the combination technique of axisymmetric solid and solid elements for three dimensional stress analysis to several other types of element combinations, such as, plate-solid, axisymmetric plate-axisymmetric solid and beam-plane stress elements. Without using the multipoint constraint equations or transition elements, this technique is also intended to deal with eigenvalue and transient analysis of compound realistic structures. At each instant, the displacement compatibility conditions at the interface between two adjacent, different type elements are still achieved through the use of the Lagrangian multiplier technique. Several numerical examples are presented to demonstrate the validity and efficiency of the technique developed. Comparisons of calculated results and the referenced solutions also show the high accuracy and advantages of this technique.