The influence of noise on the remote preparation of a qubit by an entangled pair is investigated. In Bloch sphere representation, we use the trace distance to describe how close the final state is to the original state to be prepared.Our studies include two cases. Firstly, we consider the sender and the receiver sharing a mixture of two Bell states as quantum channel in remote state preparation (RSP), and calculate the trace distance as a function of mixture ratio and angle of a state to be prepared. Secondly, the system-environment interaction is taken into account by including stochastic fluctuating terms in the system Hamiltonian. Solving the Bloch equations, we obtain the evolution density matrix of the system. We then apply this stochastic model to study the effect of noise on the trace distance of RSP.