This paper deals with a novel line balancing problem for flexible transfer lines composed of identical CNC machines. The studied lines are paced and serial, i.e. a part to be machined passes through a sequence of workstations. At least one CNC machine is installed at each workstation. The objective is to assign a given set of operations required for the machining of the part to a sequence of workstations while minimizing the total number of machines used. This problem is subject to precedence, exclusion and inclusion constraints. In addition, accessibility has to be considered. Moreover, the workstation workload depends on the sequence in which the operations are assigned because of setup times related to the change and displacement of tools, rotation of the part, etc. It is a novel line balancing problem, and we highlight its particularities by reviewing the close problems existing in the literature. Then, a mathematical model as a mixed-integer program is suggested. A procedure for computing ranges for variables is given. Experimental computations with ILOG Cplex are reported.