A mechanistic approach to formulation of the coupled problem of electrodynamics and thermomechanics is developed. Classical electrodynamics with classical physical relations is presented as a generalized theory of elasticity of 4Dmedium with anti-symmetric stress tensor, where Faraday equations are the equations of compatibility, and Ampère equations are the equations of equilibrium. It is shown that the mechanistic model of electromagnetism allows for generalization for which the tensor of the fourth rank modules in constitutive equations for extended electrodynamic formally allows not only anti-symmetric structure. We also consider the theory of space-time elasticity for 4D space-time continuum and demonstrate that it is the extended reversible thermodynamics and gives the coupled model of dynamic thermoelasticity with symmetric tensor of classical stresses and ballistic heat conductivity and involves as a particular case the traditional thermoelasticity. The presented spacetime framework we employ for studying the other coupled phenomena such as thermoelectricity or thermomagnetism. The coupled model of thermomechanics and electrodynamics is elaborated as a variational model of a two phase composite in the event space, where both phases interact at each point of the event space. It is shown that the variational method for describing connected effects and the sequential analysis of physical connectivity moduli to predict new effects of the interaction of classical electromagnetic field with spatially-isotropic material: dynamic, thermal and electrostriction. We also propose a variant of gradient formulation of the coupled problem of thermomechanics and electrodynamics, which is characterized by a significantly wider range of coupled effect.