  We introduce diagrams and Reidemeister moves for links in FxS^{1}, where F is
an orientable surface. Using these diagrams we compute (in a new way) the
Kauffman Bracket Skein Modules (KBSM) for D^{2}xS^{1} and AxS^{1}, where D^{2}
is a disk and A is an annulus. Moreover, we also find the KBSM for the
F_{0,3}xS^{1}, where F_{0,3} denotes a disk with two holes, and thus show that
the module is free.
