350 nm and 550 nm thick InGaN/GaN bilayers were irradiated with different energies (from ∼82 to ∼38 MeV) of xenon (129Xe) ions and different fluences of 1.2 GeV lead (208Pb) ions, respectively. The radiation effects of the swift heavy ions' (SHIs) bombardment were investigated using Rutherford Backscattering Spectrometry in Channeling mode (RBS/C), X-Ray Diffraction (XRD), and micro-Raman spectroscopy. To assess damage profiles, the RBS/C analysis was followed by Monte Carlo simulations using the McChasy code, revealing that InGaN is more susceptible to irradiation damage than GaN. Moreover, the simulations suggest that both randomly displaced atoms (possibly due to partial amorphization) and dislocation loops are formed. The elastic response to radiation was estimated by measuring the expansion of the c-lattice parameter. XRD revealed the presence of strain even in low fluence samples where only a small fraction of the sample volume suffered direct SHI impacts. Micro-Raman suggests that for low defect concentrations, it is dominantly biaxial, while for high defect concentrations, the simultaneous increase of hydrostatic and biaxial occurs. As a driving force of the lattice expansion, we point out the Poisson effect resulting from the pressure exerted by the SHI tracks on the surrounding undamaged crystal structure.