  A relativistic 4D string is described in the framework of the covariant
quantum theory first introduced by Stueckelberg (1941) [1], and further
developed by Horwitz and Piron (1973) [2], and discussed at length in the book
of Horwitz (2015) [3]. We describe the space-time string using the solutions of
relativistic harmonic oscillator [4]. We first study the problem of the
discrete string, both classically and quantum mechanically, and then turn to a
study of the continuum limit, which contains a basically new formalism for the
quantization of an extended system. The mass and energy spectrum are derived.
Some comparison is made with known string models.
