Summary: The effective absorption coefficient (the sink strength or the trapping constant) \(\gamma\) of a statistically isotropic random array of penny-shaped cracks is considered. The cracks are treated as oblate spheroids with vanishing aspect ratio. A variational procedure, based on Rubinstein-Torquato's principle, is employed, which yields non-trivial lower bounds on \(\gamma\) using appropriate trial fields of 'particle' and 'surface' type. The bounds include the crack-density parameter for the array as well as the two-point correlation function for the set of cracks' centres. The bounds also provide useful and non-trivial information concerning the competition of cracks at non-dilute concentration. The straightforward 'transition' of the obtained results as upper bounds on the effective permeability of an array of randomly distributed disc-like obstacles is indicated.