Abstract We focus on the random generation of SAT instances that have computational properties that are similar to real-world instances. It is known that industrial instances, even with a great number of variables, can be solved by a clever solver in a reasonable amount of time. This is not possible, in general, with classical randomly generated instances. We provide different generation models of SAT instances, extending the uniform and regular 3-CNF models. They are based on the use of non-uniform probability distributions to select variables. Our last model also uses a mechanism to produce clauses of different lengths as in industrial instances. We show the existence of the phase transition phenomena for our models and we study the hardness of the generated instances as a function of the parameters of the probability distributions. We prove that, with these parameters we can adjust the diffificulty of the problems in the phase transition point. We measure hardness in terms of the performance of different solvers. We show how these models will allow us to generate random instances similar to industrial instances, of interest for testing purposes