A predictive correlation between hard cosmic ray flux (HCRF) near the Earth's surface and sudden increases in the number of cases of cardiovascular disease (CVD) was studied in Vilnius city. Gamma spectrometers were used to measure HCRF. Changes in the total number of impulses registered by these devices were taken as the physical parameter for prediction of an increase in the number of CVD cases. For quantitative assessment of CVD dynamics two empirical criteria for HCRF were proposed: (1) a consistent fall in the HCRF by 200 or more impulses for 4 or more hours per day; (2) the difference (no less than 15 impulses per hour) between the average number of impulses registered in 2 (subsequent and previous) days. The periods analyzed were those when the number of CVD cases exceeded the average monthly level by 10% and 15%. HCRF fluctuations were used as an indirect indicator of variations in the geomagnetic field, and a leap in CVD cases was predicted 1-3 days following a change in the HCRF according to the two criteria mentioned above. The predictive reliability of an increase in CVD cases within 2-3 days exceeded 80%, and within 1-2 days 70%. No essential difference in predictive reliability was observed when the number of CVD cases exceeded the average monthly level by 10% or 15%. Geomagnetic field variations contribute only insignificantly to leaps in the number of CVD cases, which are evoked by the sum effects of other factors. The results of the present study should be regarded as preliminary.