Thermoelectric power (TEP) of YBa2Cu3O7-X (123) and YBa2Cu4O8 (124) samples are measured as a function of pressure. The TEP of an as-sintered 123 polycrystalline sample shows a broad maximum around 1.25 GPa whereas that of the cold-pressed sample decreases steadily. The ab-plane TEP of 123 single crystal decreases monotonically and the c-axis TEP exhibits a maximum around 1.5 GPa. Disappearance of the broad maximum in the polycrystalline sample upon cold-pressing is interpreted in terms of the crystallite orientation occurring under pressure. TEP of the 124 polycrystalline sample decreases sharply up to 4.5 GPa and at a lower rate with further increase in pressure, a trend similar to that is observed in the variation of Tc as a function of pressure.