APEmille is a SIMD parallel processor under development at the Italian National Institute for Nuclear Physics (INFN). It is the third machine of the APE family, following Ape and Ape100. APEmille is well suited for Lattice QCD applications, climate modelling, neural networks, computational chemistry, numerical wind tunnels, seismic and combustion simulation. APEmille is a tridimensional array of custom processors each with peak performance of 528Mflop and 8-32 Mbytes of locally addressable RAM. The 2048-processor machine reaches the performance of 1.081Tflops. APEmille is interfaced to the external world through a PCI interface. A powerful programming language named TAO is provided. A C++ compiler is foreseen.