Purpose - The purpose of the paper is to investigate the linear thermal buckling and vibration analysis of layered and multiphase magneto-electro- elastic (MEE) cylinders made of piezoelectric/piezomagnetic materials using finite element method. Design/methodology/approach - The constitutive equations of MEE materials are used to derive the finite element equations involving the coupling between mechanical, electrical, magnetic and thermal fields. The present study is limited to clamped-clamped boundary conditions. The linear thermal buckling is carried out for an axisymmetric cylinder operating in a steady state axisymmetric uniform temperature rise. The influence of stacking sequences and volume fraction of multiphase MEE materials on critical buckling temperature and vibration behaviour is investigated. The influence of coupling effects on critical buckling temperature and vibration behaviour is also studied. Findings - The critical buckling temperature is higher for MEE axisymmetric cylinder as compared to elastic cylinder. Originality/value - Linear thermal buckling and vibration analysis of MEE axisymmetric cylinders are studied using the finite element approach. The structure can be used for active vibration control, sensors and actuators. Studying the buckling and vibration behaviour of such structures and influence of coupling effect is extremely useful for the design of magnetoelectroelastic structures. © Emerald Group Publishing Limited.