Cross-medium missiles possess the characteristics of fast speed， long range， and strong surprise attack across airspace and water bodies， leading to ineffective close-range aerial interception against them， short interception reaction time and high defense difficulty through hard killing methods at the end of the cross-medium trajectory. This article focuses on the key issues of anti-cross-medium missile interception. Firstly， the ballistic attack characteristics of cross medium missiles after crossing domains are summarized and analyzed. Then， three interception ballistic strategies， namely advance angle guidance， maneuvering occupancy， and zero control optimization， are proposed to meet the defense requirements of early interception， rapid interception， and precise interception under different situational conditions. The interception efficiency of different ballistic models is compared and analyzed through simulation experiments， showing that the interception probability of the zero control optimal interception strategy is relatively high and stable in various situations with interception efficiency higher than 90%； the interception probability of the maneuver occupying interception strategy is moderate but less affected by the situation， and the interception efficiency ranges from 50% to 80%； the advanced angle guidance interception strategy method achieves interception efficiency above 70% in all situations， especially in close range and medium angle situations， whereas the situation has a significant impact on interception probability. It has been shown that this paper provides a solid reference for in-depth research on the design of interception trajectories for the rapid and efficient defense of cross medium missiles and anti-cross-medium missiles.