The network tied-arch bridge has become a common bridge type for short and medium span bridges. Several articles have been published focused on the comparison of the traffic load bending moments between network tied-arch arch bridges and traditional tied-arch bridges as well as on the selection of the most advantageous hanger network. This article presents the calculation of the shape of a constant stress network tied-arch bridge based on graphical statics and vector algebra. For the bridge the quantities of the steel arch, tie tendons and hangers and their costs are calculated according to the span-rise ratio. The cost-optimal height for the arches is calculated too. The increase in the construction cost due to the height of the arch is considered quadratically. This study shows that the cost-optimal height of the bridge decreases when the of the bridge span length increases. The presented calculations are made for the iterated moment-less constant stress arch shape and by using selected stress values, corresponding to the permanent loads. The calculation procedure is an efficient method in the preliminary design of network tied-arch bridges. The needed data is minimal. The calculation of the arch is an important task also in network tied-arch bridges to avoid unnecessary permanent bending stresses.