  The Mathisson-Papapetrou method is originally used for derivation of the
particle world line equation from the covariant conservation of its
stress-energy tensor. We generalize this method to extended objects, such as a
string. Without specifying the type of matter the string is made of, we obtain
both the equations of motion and boundary conditions of the string. The world
sheet equations turn out to be more general than the familiar minimal surface
equations. In particular, they depend on the internal structure of the string.
The relevant cases are classified by examining canonical forms of the effective
2-dimensional stress-energy tensor. The case of homogeneously distributed
matter with the tension that equals its mass density is shown to define the
familiar Nambu-Goto dynamics. The other three cases include physically relevant
massive and massless strings, and unphysical tahyonic strings.
