In this paper we first propose a new reaching law for discrete time sliding mode control of linear time-invariant systems subject to disturbance and modelling uncertainty. The reaching law makes the sliding variable rate of change proportional to the inverse tangent of this variable, which results in bounded state and control effort. Then we apply the proposed reaching law to design an efficient flow control strategy for multi-source connection oriented (for example ATM or MPLS) data transmission networks. The strategy ensures full exploitation of the available bandwidth and eliminates the risk of data loss in the network. Moreover, the strategy proposed in this paper generates bounded data transmission rates which are limited by design parameters and do not depend on the initial state of the network.