This study presents gelatine-based and agar-based phantoms with an addition of glycerol, safflower oil, silicone oil and cellulose microcrystalline with a potential to cover the entire range of tissue diffusion coefficients and kurtosis values. Forty types of phantoms were prepared and examined for NMR relaxation times T₁ and T₂ and diffusional metrics D, K and ADC. Wide ranges of values of D (0.0003–0.0031 mm²s⁻¹), K (0.00–7.24) and ADC (0.0002–0.0031 mm²s⁻¹) were observed. Two of the phantoms closely mimic muscle and cortical gray matter with respect to water diffusion parameters. Although many of the presented phantoms display both D and K values within the range of human tissues, they match different tissues with respect to D and K. The imaging results for the gray matter simulating phantom injected with the liposomal solution, bear a resemblance to the particle size effect described in the literature. The phantoms presented in this work are simple in preparation and affordable tissue-simulating materials to be used primarily in development of diffusion kurtosis-based MRI methods and possibly in a preliminary assessment of MRI contrast agents. Further adjustments of the chemical compositions could potentially lead to development of new types of phantoms mimicking diffusional properties of more kinds of soft tissues.