We present a novel Monte-Carlo lattice model for the study of the coil-stretch transition for polymer chains in deformation flows. Our results indicate that elongational flows are much more effective than shear flows in stretching polymer chains, in full agreement with experimental observation. Our model data also show that the (epsilon) over dot(c)similar to M-1.5 powerlaw observed experimentally for the dependence of critical flow rate on polymer molecular weight can be fully explained through a nonuniform stretching of the chain by the flow. A higher powerlaw exponent is predicted in more affine deformation cases.