A line balancing problem for transfer machines with rotary tables is considered. This type of machine is used in mass production. A part is sequentially machined on m working positions and is moved from one position to the next using a rotary table. The operations are grouped into blocks, where the operations of the same block are simultaneously performed by one piece of equipment with several tools (a multi-spindle head). All multi-spindle heads of a machine are simultaneously activated. Therefore, all operations of the machine are executed in parallel on m parts mounted on the rotary table. The line balancing problem consists of partitioning the set of all operations into sub-sets in order to minimize the number of working positions and the total number of spindle heads while satisfying all the constraints (precedence, compatibility for spindle heads, etc.). The method proposed in this paper is based on transforming this line balancing problem into a search for a constrained shortest path. An algorithm for simultaneously generating a graph and finding a constrained shortest path is developed. Some dominance rules for reducing the graph size are provided. An industrial example is presented in detail and experimental results on other industrial instances are reported.