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 stations. At least one CNC machine (Computer Numerical Controller machine) is installed at each station. The objective is to assign a given set of operations required for part machining to a sequence of stations while minimizing the total number of machines used. This problem is subject to precedence constraints as well as exclusion and inclusion constraints. Moreover, the station workload depends on the sequence in which the operations are assigned to the station because of setup times related to the change and displacement of tools, rotation of the part, etc. In addition, accessibility constraints have to be considered. Therefore, it is a novel problem in the class of line balancing problems. In this paper, we highlight its particularities by reviewing the close problems existing in the literature. Then, we suggest a mathematical model as a mixed-integer program for the formulation of the problem as well as a procedure for computing ranges for variables. Experimental computations with ILOG Cplex are reported.