We study multiply warped product geometries MN:=Bn×Fn1×···×FnAg = g_B + \sum_{a=1}^A v_a^2 g_{F^{n_a}} and show that for an open set of initial data within multiply warped product geometries the Ricci flow starting at any of those develops generalized cylinder as singularity model. More precisely, for any p and q we construct an open set of initial data within multiply warped product geometris whose Ricci flows develop S^p\times R^q as a singularity model.