Computational and Applied Mathematics is becoming one of the main driving forces of the current development of Applied Sciences. Modeling, Analysis and Computer Simulation based on advanced mathematical methods is absolutely necessary in most fields of science and engineering. The Department of Applied Mathematics (DApplM) at the University of Crete (UoC) over the course of its 10 years of existence has attracted a number of Greek Applied mathematicians mostly from outside Greece, and is currently the main unit that centers its activity on modern applied mathematics in Greece. The key concept behind this project is that in order to strengthen the research profile of the Applied Mathematics Department and to enable its members to enhance their contacts with major research centers in Europe, certain measures need to be taken that will reinforce the Department’s research capability in areas where it has recognized expertise. These measures are organized around a proposed Center, named Archimedes Center for Modeling, Analysis, and Computation (ACMAC), aiming to promote academic excellence in Applied Mathematics and fostering the interface of modeling, analysis and computation.