  Continuum equations are ubiquitous in physical modelling of elastic, viscous,
and viscoelastic systems. The equations of continuum mechanics take nontrivial
forms on curved surfaces. Although the curved surface formulation of the
continuum equations are derived in many excellent references available in the
literature, they are not readily usable for solving physical problems due to
the covariant, contravariant or mixed nature of the stress and strain tensors
in the equations. We present the continuum equations in terms of physical
components in a general differentiable manifold. This general formulation of
the continuum equations can be used readily for modelling physical problems on
arbitrary curved surfaces. We demonstrate this with the help of some examples.
