The study aims to identify the aging characteristics of hard and soft wheat caryopses without treatment and following treatment with pulse pressure created by a shock wave. The grain was treated with pulse pressures of 11 and 29 MPa. After one month and after three years, the caryopses were sorted into vitreous and floury types. The germination of control soft wheat caryopses decreased after storage, while after pulse pressure treatment and storage, it exceeded that of the control. The germination of control hard wheat caryopses with floury endosperm decreased after storage to a greater extent than that of caryopses with vitreous endosperm. Pulse pressure treatment reduced the germination of caryopses with vitreous endosperm. No change was observed in the protein content of control hard wheat caryopses following prolonged storage. In this case, pulse pressure contributed to the reduction in protein content during storage. The protein content of soft wheat caryopses with floury endosperm decreased after storage. In these caryopses, pulse pressure treatment contributed to better protein retention. Thus, the caryopses of hard wheat and soft wheat with vitreous endosperm were less susceptible to aging as compared to the caryopses of soft wheat and caryopses with floury endosperm, respectively. Pulse pressure damaged the vitreous endosperm, accelerating seed aging. It also contributed to the long-term storage of soft wheat caryopses without a significant loss of viability. Thus, it is possible to treat soft wheat grain to extend its shelf life.