In accordance with the difficulties posed by the substantial usage of computing resources for simulation methods， this study presents an analytic model that specifically examines the effectiveness of long-range torpedo anti-submarine search operations. The dispersion of target locations during patrol search and on-call search is meticulously examined， taking into consideration the tactical requirements and the detection principle in the process of long-range torpedo attack. Furthermore， the analytic model of long-range torpedo anti-submarine search effectiveness is constructed with the detection probability serving as the primary indicator. Realistic anti-submarine combat scenarios are employed to apply both the analytic model and simulation method， which results in a simulation test of the long-distance torpedo anti-submarine search. The findings of the test reveal that patrol search efficiency improves with an increase in the number and average speed of long-range torpedoes， but decreases with an increase in the mission area. On the other hand， on-call search efficiency improves with an increase in the average speed of long-range torpedoes. The calculated values derived from the model align well with the results of the simulation method.