A three-component model of the solar chromosphere, developed from ground based observations of the Ca II K chromospheric emission, is used to calculate the variability of the Lyman alpha flux between 1969 and 1980. The Lyman alpha flux at solar minimum is required in the model and is taken as 2.32¿1011 photons/cm2/s. This value occurred during 1975 as well as in 1976 near the commencement of solar cycle 21. The model predicts that the Lyman alpha flux increases to as much as 5¿1011 photons/cm2/s at the maximum of the solar cycle. The ratio of the average fluxes for December 1979 (cycle maximum) and July 1976 (cycle minimum) is 1.9. During solar maximum the 27-day solar rotation is shown to cause the Lyman alpha flux to vary by as much as 40% or as little as 5%. The model also shows that the Lyman alpha flux varies over intermediate time periods of 2 to 3 years, as well as over the 11-year sunspot cycle. We conclude that, unlike the sunspot number and the 10.7-cm radio flux, the Lyman alpha flux had a variability that was approximately the same during each of the past three cycles. Lyman alpha fluxes calculated by the model are consistent with measurements of the Lyman alpha flux made by 11 of a total of 14 rocket experiments conducted during the period 1969--1980. The model explains satisfactorily the absolute magnitude, long-term trends, and the cycle variability seen in the Lyman alpha irradiances by the OSO 5 satellite experiment. The 27-day variability observed by the AE-E satellite experiment is well reproduced. However, the magntidue of the AE-E 1 Lyman alpha irradiances are higher than the model calculations by between 40% and 80%. We suggest that the assumed calibration of the AE-E irradiances is in error.