A variety of new porous materials with unusually small pores have been manufactured in the past decades. To predict their acoustical properties, the conventional models need to be modified. When pore size becomes comparable to the molecular mean free path of a saturating fluid, the no-slip conditions on the pore surface are no longer accurate and hence the slip effects have to be taken into account. In this paper, sound propagation in microfibrous materials is modeled analytically, approximating the geometry by a regular array of rigid parallel cylinders. It has been shown that velocity and thermal slip on a cylinder surface significantly changes the model predictions leading to lower attenuation coefficient and higher sound speed values. The influence of material porosity, fiber orientation, and size on these effects is investigated. Finite element method is used to numerically solve the oscillatory flow and heat transfer problems in a square array of cylindrical fibres. Numerical results are compared with predictions of the analytical model and the range of its validity is identified.