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Application of superconducting magnets to magnetic confinement fusion reactors is necessary to generate as strong magnetic field as possible since a huge amount of electrical power is consumed if normal conducting magnets are used. And the strong field from the superconducting magnets generates very large electromagnetic force into structural components. It is thus required to establish a design guideline for the superconducting magnet structures. Development of a computer code to calculate stress-strain state in the complex interior of the magnet could serve the requirements.In this paper mathematical formulations available for the finite element implementation are presented to solve detailed stress and strain in layered components of the magnets. The formulations are based on the composite theory of layered structures. Examples of numerical analysis are presented for electromagnetomechanical analysis of toroidal coils of the R-machine which has been discussed and promoted by Institute of Plasma Physics, Nagoya University. The numerical results are compared with those obtained from the beam-shell model. Significant differences are found at some portions between them indicating validity of the present code "MAGCOMP". Detailed stress distributions are shown for each component, which would be furthermore available to analysis and evaluation of quench phenomena.