Fault detection and isolation is a ubiquitous task in current complex systems even in the linear networked case when the complexity is mainly caused by the complex network structure. A simple yet practically important special case of networked linear process systems is considered in this paper with only a single conserved extensive quantity but with a network structure containing loops. These loops make fault detection and isolation challenging to perform because the effect of fault is propagated back to where it first occurred. As a dynamic model of network elements, a two input single output (2ISO) LTI state-space model is proposed for fault detection and isolation where the fault enters as an additive linear term into the equations. No simultaneously occurring faults are considered. A steady state analysis and superposition principle are used to analyse the effect of faults in a subsystem that propagates to the sensors’ measurements at different positions. This analysis is the basis of our fault detection and isolation procedure that provides the position of the faulty element in a given loop of the network. A disturbance observer is also proposed to estimate the magnitude of the fault inspired by a proportional-integral (PI) observer. The proposed fault isolation and fault estimation methods have been verified and validated by using two simulation case studies in the MATLAB/Simulink environment.