A solution describing the configuration of a uniformly accelerated str
ing is found in a Rindler space modified by a maximal acceleration. We
find a critical value of string acceleration less than the maximal on
e which depends on the distance L between the ends of the string. Even
in the limit in which L --> 0 a finite maximal acceleration exists fo
r a particle, and the string size for the accelerated observer stays f
inite.