The central notion of conflict in drama is well-acknowledged but not properly formalized. Computational models of conflict tend to target one specific type of conflict and consequently lose the global point of view on the story. Using a model of dramatic structure, this article specifies a number of conflict types within a unified model and proposes an algorithm to automatically extract all conflicts within a narrative structure. The algorithm is then tested on a storyworld that shows as many as 31 coexisting conflicts. Finally, a cluster analysis on these conflicts is performed, showing that in the considered case, conflicts can be reduced to three main “conflict groups.”