Cover systems used on machinery can be an important contributor to noise reduction. The design and evaluation of cover systems is largely experimental, as exact theoretical evaluation is generally considered impossible. Architectural acousticians have made use of statistical procedures that ignore acoustical-wave characteristics to determine approximate reverberation and sound levels. These procedures can be extended to approximately describe the problem of enclosures. A severe limitation is that cover geometry is not considered. Markov-chain procedures were used to describe geometric cover effects. An absorbing Markov chain was formulated to describe statistically the passage of an acoustical energy “bundle” from machine source, through a three-dimensional cover system, to external locations. The source directivity, and cover absorption, and transmission-loss coefficients are required input in addition to cover geometry. A procedure was devised and programmed for an IBM-7094 to manipulate mathematically the Markov chain to determine a statistical approximation of cover attenuation to these external locations. Experimental investigation of model cover systems was used to varify and improve the procedure.