The oil industry has always invested in research in order to optimize drilling operation. The aim is to develop technology to increase the rate of penetration and reduce the non-productive time during drilling. The recent discovery of large oil reserves located in very deep layers that are covered with thick salt layers has increased the importance of studies associated with drilling optimization in Brazilian offshore sub-salt oil fields. There are many models to predict rate of penetration based on operational parameters, drill bit type and rock properties. The specific mechanical energy is the parameter often used as reference to guide the efficiency of the drilling operation as well as to identify what has to be changed in order to improve the drilling. This dissertation analyses different methods for drilling optimization based on the specific mechanical energy. These methods are applied to a data set that consists of drilling parameters (weight-onbit, torque, rate of penetration, rotation per minute) for 6 wells along the sections of evaporites. Large-scale drilling experiments carried out at the laboratory were also used. The study concludes that the ideal specific mechanical energy on most operations is related to a fraction of the confined compressive strength of the rock.