The novel non-combustible sandwich panel is extremely fragile in manufacturing and cannot be tensioned between rolls. Previous studies on the roll-to-roll system, which mainly focused on the high-tension situations and little described the low-strength materials, are insufficient. To explore the transportation of low-strength materials, we study the tension distribution of continuous moving flexible one-dimensional materials on a steady-state track. First, we propose a numerical method to calculate the steady-state track of low-strength sheet between rolls considering the gravity, as well as size and position of rolls. Then we obtain the optimum sag at different size and position of rolls. We find out that there is a lower limit of the sheet’s strength-density ratio (the Minimum Specific Strength) for a specific set of size and position of rolls. Finally, we establish a method to calculate the lower limit approximately for engineering use. Our method can be generalized in manufacturing other low-strength flexible thin-sheet materials as well.