Context : Aims : We determine the central mass distribution of galaxy cluster RX J1347 - 1145 using strong gravitational lensing . Methods : High resolution HST/ACS images of the galaxy cluster RX J1347 - 1145 have enabled us to identify several new multiple image candidates in the cluster , including a 5 image system with a central image . The multiple images allow us to construct an accurate 2-dimensional mass map of the central part of the cluster . The modelling of the cluster mass includes the most prominent cluster galaxies modelled as truncated isothermal spheres and a smooth halo component that is described with 2 parametric profiles . The mass reconstruction is done using a Markov chain Monte Carlo method that provides us with a total projected mass density as well as estimates for the parameters of interest and their respective errors . Results : Inside the Einstein radius of the cluster ( \sim 35 ^ { \prime \prime } , or \sim 200 kpc , for a source at redshift 1.8 ) we obtain a total mass of ( 2.6 \pm 0.1 ) \times 10 ^ { 14 } M _ { \odot } . The mass profile of the cluster is well fitted by both a Navarro , Frenk and White profile with a moderate concentration of c = 5.3 ^ { +0.4 } _ { -0.6 } and r _ { 200 } = 3.3 ^ { +0.2 } _ { -0.1 } Mpc , or a non-singular isothermal sphere with velocity dispersion \sigma = 1949 \pm 40 km/s and a core radius of r _ { c } = 20 \pm 2 ^ { \prime \prime } . The mass profile is in reasonable agreement with previous mass estimates based on the X-ray emission from the hot intra-cluster gas , however the X-ray mass estimates are systematically lower than what we obtain with gravitational lensing . Conclusions :