  We consider the effects of going beyond the approximation of a straight
string in mesons by using a flexible flux tube model wherein a Nambu-Goto
string bends in response to quark accelerations. The curved string is
dynamically identical to the straight string even for ultra-relativistic mesons
except for a small additional radial momentum. We numerically solve the curved
string model in the case where both ends have equal mass quarks and also the
case where one end is fixed. No approximation of non-relativistic motion is
made. We note some small but interesting difference from the straight string.
