The effective absorption coefficient (the sink strength or the trapping constant) γ 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'principle, is employed, which yields non–trivial lower bounds on γ 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.