The pressure dependence of the total magnetic susceptibility per unit volume, dlnchi T/dP, has been measured in the alkali metals at pressures up to 140 MPa, using a SQUID magnetometer. The values obtained for Na, K, Rb and Cs are 0.13+or-0.20, 6.42+or-0.95, 5.46+or-0.45 and 15.59+or-0.53 in units of 10-10 Pa-1, corresponding to values of dlnchi T/dln V of 0.10+or-0.14, -2.46+or-0.38, -1.71+or-0.14 and -3.73+or-0.14 respectively. In Na and K, values of dlnchi P/dln V deduced from dlnchi T/dln V are discussed in relation to the theory by L. Wilk et al. (1979). Good agreement is found between the experimental and theoretical values, supporting their conclusion that the ion core and crystalline effects must be taken into account in calculations of the spin susceptibility. In Li, for which measurements have not been made in the present work, the theory leads to a rather larger value for the volume dependence of chi P than is deduced from CESR work by T. Kushida et al. (1979). There have been no corresponding theoretical calculations for Rb and Cs and the discussion of the values of dlnchi P/dln V obtained here is limited to a consideration of relativistic effects and of effects due to the proximity of the 5d band to the Fermi level. In addition to dlnchi T/dP, chi T has also been measured for Na, K, Rb and Cs and the resultant volume susceptibilities are: +7.61+or-0.20, 5.18+or-0.19, 4.24+or-0.16 and 5.36+or-0.21*10-6 SI units respectively. These measurements were made because the values for chi T in the literature show a wide spread, and accurate value is needed for analysis of the data.