Zeolites are crystalline aluminosilicate minerals featuring a network of 0.3-1.5-nm-wide pores, used in industry as catalysts for hydrocarbon interconversion, ion exchangers, molecular sieves and adsorbents. For improved applications, it is highly useful to study the distribution of internal local strains because they sensitively affect the rates of adsorption and diffusion of guest molecules within zeolites. Here, we report the observation of an unusual triangular deformation field distribution in ZSM-5 zeolites by coherent X-ray diffraction imaging, showing the presence of a strain within the crystal arising from the heterogeneous core-shell structure, which is supported by finite element model calculation and confirmed by fluorescence measurement. The shell is composed of H-ZSM-5 with intrinsic negative thermal expansion whereas the core exhibits a different thermal expansion behaviour due to the presence of organic template residues, which usually remain when the starting materials are insufficiently calcined. Engineering such strain effects could have a major impact on the design of future catalysts.