It depends on the analysis you want to do. If you are interested in only the compliance of the cylinder, the standard 8-node isoparametric shell or plate element should be adequate.
If you are worried about the stresses in the vicinity of the cuts, you might want to use solid (brick) elements.
If the compression direction is parallel to the axis of the cylinder and the cuts in the wall are designed to make the cylinder compliant along this axis, you may want to consider performing a buckling analysis if the remaining "beams" are loaded in pure compression.
Alternately, if you need compliance along the axial direction, you might want to design the cuts so that the remaining beams are loaded in shear or bending.
pj