This paper presents an experimental study on the penetration characteristics of submillimeter waves in biological tissues and material. The measured values of the penetration depth in excised natural muscle, fat, and aqueous solution of protein, bovine serum albumin (BSA), over the wavelengths of 281 through 496µm are presented. Penetration depths at these wavelengths are 0.11-0.17mm in the natural pork muscle, and 0.69-0.98mm in the natural pork fat, and are the larger at the longer wavelengths. The values vary considerably from sample to sample. Since the measurement of the penetration depth in this study is shown sufficiently reproducible, the variation of the measured penetration depth is attributed to the variation of natural tissues such as that in water content. It is found that the penetration depth of submillimeter waves in aqueous solution of BSA depends almost linearly on the amount of protein content in the solution, and that the typical values of the penetration depth in the natural muscle roughly agree with that in the 35% aqueous solution of BSA in the submillimeter-wave region.