We study the thermodynamic properties of a semiexible polymer confined inside strips of widths L <= 9 defined on a square lattice. The polymer is modeled as a self-avoiding walk and a short-range interaction between the monomers and the walls is included through an energy <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">associated with each monomer placed on one of the walls. Also, an energy <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">b is associated with each elementary bend of the walk. The free energy of the model is obtained exactly through a transfer matrix formalism. The profile of monomer density and the force on the walls are obtained. We notice that as <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">b is decreased, the range of values of <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">which the density profi le is neither convex nor concave increases, and for sufficiently attracting walls (<IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif"> < 0) we find that in general the attractive force is maximum for <IMG SRC="/img/fbpe/bjp/v32n4/a19img04.gif">b < 0, that is, for situations where the bends are favored.