The paper deals with characterisation and modelling of laser milling process on Silicon Carbide hard ceramic. To this end, a Yb:YAG pulsed fiber laser was adopted to mill Silicon Carbide bars. Square pockets, 5x5 mm2 in plane dimension, were machined at the maximum nominal average power (30W), under different laser process parameters: pulse frequency, scan speed, hatching distance, repetitions and scanning strategy. After machining, the achieved depth and the roughness parameters were measured by way of digital microscopy and 3D surface profiling, respectively. In addition, the material removal rate was calculated as the ratio between the removed volume/process time. ANalysis Of VAriance (ANOVA) was adopted to assess the effect of the process parameters on the achieved depth, the material removal rate (MRR) and roughness parameters, while Response Surface Methodology (RSM) and Artificial Neuronal Networks (ANNs) were adopted to model the process behaviours. Results show that both RSM and ANNs fault in MRR and RSm roughness parameters modelling. Thus, an integrated approach was developed to overcome the issue; the approach is based on the use of the RSM model to obtain a hybrid Training dataset for the ANNs. The results show that the approach can allow improvement in model accuracy.