Fluid-structure interaction (FSI) problems involving thin slender bodies are a difficult modelling problem particularly for highly flexible bodies. An accurate, numerically stable approach is presented for fixed bodies as a first stage where weakly compressible smoothed particle hydrodynamics in Eulerian form (EWCSPH) is coupled with the immersed boundary method (IBM) and applied to the problems of an accelerating square box, as a non-slender case, and an impulsively started flat plate as a slender body case. The results for the box case show that vortical flow structures are virtually identical to those predicted by industry standard finite-volume solvers for lower Reynolds numbers (up to 150). For a higher Reynolds number of 450 there is some evidence that EWCSPH provides more accurate vortical structures for equivalent mesh/particle resolutions. Computational resource requirements are similar. The results for the plate case demonstrate that to simulate strong dynamic shear layers and vortex shedding the Eulerian form of SPH offers significantly greater stability and accuracy in comparison to the conventional Lagrangian form.