  The Casimir energy for the transverse oscillations of a piecewise uniform
closed string is calculated. The great adaptibility of this string model with
respect to various regularization methods is pointed out. We survey several
regularization methods: the cutoff method, the complex contour integration
method, and the zeta-function method. The most powerful method in the present
case is the contour integration method. The Casimir energy turns out to be
negative, and more so the larger is the number of pieces in the string. The
thermodynamic free energy F is calculated for a two-piece string in the limit
when the tension ratio x=T_{I}/T_{II} approaches zero.
