Future machine to machine (M2M) communications need to support a massive number of devices communicating with each other with little or no human intervention. Random access techniques were originally proposed to enable M2M multiple access, but suffer from severe congestion and access delay in an M2M system with a large number of devices. In this paper, we propose a novel multiple access scheme for M2M communications based on the capacity-approaching analog fountain code to efficiently minimize the access delay and satisfy the delay requirement for each device. This is achieved by allowing M2M devices to transmit at the same time on the same channel in an optimal probabilistic manner based on their individual delay requirements. Simulation results show that the proposed scheme achieves a near optimal rate performance and at the same time guarantees the delay requirements of the devices. We further propose a simple random access strategy and characterized the required overhead. Simulation results show the proposed approach significantly outperforms the existing random access schemes currently used in long term evolution advanced (LTE-A) standard in terms of the access delay.