We present mass reconstructions from weak lensing for the galaxy clusters A1835 and A2204 over 34' x 34' fields using data from the ESO/MPG Wide Field Imager. Using a background galaxy population of 22 < R < 25.5 we detect the gravitational shear of A1835 at 8.8sigma significance, and obtain best-fit mass profiles of sigma(v) = 1233(-70)(+66) km s(-1) for a singular isothermal sphere model and r(200) = 1550 h(-1) kpc, c = 2.96 for a "universal" CDM profile. Using a color-selected background galaxy population of 22 < R < 25.8 we detect the gravitational shear of A2204 at 7.2sigma significance, and obtain best-fit mass profiles of sigma(v) = 1035(-71)(+65) km s(-1) for a SIS model and r(200) = 1310h(-1) km s(-1), c = 6.3 for a "universal" CDM profile. The gravitational shear at distances greater than 10' is significantly detected for both clusters. The best fit weak lensing cluster masses agree well with both X-ray and dynamical mass measurements, although the central concentration of A1835 is much lower in the weak lensing mass profile than that measured by recent Chandra results. We suggest that this lower concentration is most likely a combination of contamination of the "background" galaxy population with cluster dwarf galaxies and the effect of a prolate or tri-axial cluster core with the major axis lying near the plane of the sky. We also detect a number of additional structures at moderate significance, some of which appear to be sub-haloes associated with the clusters.