We consider the effects of going beyond the approximation of a straight str
ing in mesons by using a flexible flux tube model wherein a Nambu-Goto stri
ng bends in response to quark accelerations. The curved string is dynamical
ly identical to the straight string even for ultra-relativistic mesons exce
pt for a small additional radial momentum We numerically solve the curved s
tring model in the case where both ends have equal moss quarks and also in
the case where one end is fixed. No approximation of non-relativistic motio
n is made. We note some small but interesting differences from the straight
string. [S0556-2821(99)07419-6].