An analysis of the con.nement losses in photonic crystal fibers due to the finite numbers of air holes is performed by means of the finite element method. The high flexibility of the numerical method allows us to consider fibers with regular lattices, like the triangular and the honeycomb ones, and circular holes, but also fibers with more complicated cross sections like the cobweb fiber. Numerical results show that by increasing the number of air hole rings the attenuation constant decreases. This dependence is very strong for triangular and cobweb fibers, whereas it is very weak for the honeycomb one.