A braiding machine for that produces three-dimensional braided matrices with a suitable pore structure for even and random distribution and in-growth of cells for tissue growth and repair is described herein. Methods for making three-dimensional matrices with controlled thicknesses and porosity and the resulting matrices are also described. The machine contains curved arches that hold the plurality of carriers. At least two of the arches are moveable in a side-to-side direction. Additionally, a controlled pushing mechanism pushes the carriers up and down the slots in the arches. These motions allow one to form three-dimensional braided matrices that provide sufficient porosity and mechanical support for tissue growth and repair in a variety of sites in the body.
