Abstract--- In this paper we describe a computational model oriented to the efficient processing of dense matrices using a parallel and linear recursive synchronous computing approach. The architecture, design, and performance of this conceptual model are described; it is denominated the Parallel and Recursive Computing Model or PRCM. This model has been used to address the problem of function list evaluation. The model is based on important computational notions such as parallelism and recursion theory, which govern both its organization and operation mode. Fine-grain parallelism is exploited by means of synchronous processing across processor pipelines; concurrency and execution control are achieved via dataflow. The structure of the PRCM is organized as a stack of recursive levels that control the massive processing of dense matrices as a large list of linear recursive functions. Keywords— Computing model, Matrix multiplication algorithm, Parallel recursive computing, Linear recursive function, Pipeline,Dataflow.