The presence of a universal machine model for serial algorithm design, namely the von Neumann model, has been one of the key ingredients of the success of uniprocessors. The presence of such a model makes it possible for an algorithm to be ported across a wide range of uniprocessors efficiently. Universal algorithm design models proposed for parallel computers however tend to be limited in the range of parallel platforms they can efficiently cover. Consequently, portability of parallel programs is attained at the expense of loss of efficiency. In this paper, we explore desirable and attainable properties of universal models of architecture independent parallel program design. We study various models that have been proposed, classify them based on important machine parameters and study their limitations.