Intracellular processes of live organisms, which can be described by sets of biochemical reactions, are inherently stochastic, where the fluctuations in molecule abundance inside the cell play a crucial role in the cellular growth and development. For typical building blocks of biochemical reaction networks （including signal transduction networks and metabolic networks）, this paper first gives a unified formulation and then presents a general mechanism of noise propagation by applying the linear noise approximation theory. The main results show that: there is noise propagation in signaling transduction pathways and the noise intensity satisfies noise sum rule, and there is no noise propagation in metabolic pathways and the distributions of the steady state molecules mutually independent. The analytical results lay a theoretical foundation for understanding the intracellular processes.