The existence of Gliese 581c and its mass have been measured by the radial velocity method of detecting extrasolar planets. The mass of a planet is calculated by the small periodic movements around a common centre of mass between the host star Gliese 581 and its planets. When all six planets are fitted with a Keplerian solution, the minimum mass of the planet is determined to be 5. 5 Earth masses. The radial velocity method cannot by itself determine the true mass, but it cannot be very much larger than this or the system would be dynamically unstable. Dynamical simulations of the Gliese 581 system which assume the orbits of the planets are coplanar indicate that the planets cannot exceed approximately 1. 6 to 2 times their minimum masses or the planetary system would be unstable (this is primarily due to the interaction between planets e and b). For Gliese 581c, the upper bound is 10. 4 Earth masses.