A monolithic projection framework for constrained fluid–structure interaction (CFSI) problems is proposed to solve multi-structure and multi-constraint problems. Immersed boundary method (IBM) in the continuous forcing form is used to evaluate the constraint force on the fluid–structure interface due to the no-slip boundary condition. Besides, constraints from material properties and inter-structure dynamics are uniformly considered. All subsystems are assembled into a monolithic system and solved efficiently with approximate LU decomposition. Simulations of the flapping filament, flapping flag, windsock waggling and parachute deploying cases are conducted to examine the accuracy, efficiency and capability for bilateral and unilateral constraints of the FSI systems, respectively. The results show nearly second-order accuracy temporally, along with significant efficiency improvement.