The general position problem is to find the cardinality of the largest vertex subset S S such that no triple of vertices of S S lies on a common geodesic. For a connected graph G G , the cardinality of S S is denoted by gp ( G ) {\rm{gp}}\left(G) and called the gp {\rm{gp}} -number (or general position number) of G G . In the paper, we obtain an upper bound and a lower bound regarding the gp {\rm{gp}} -number in all cacti with k k cycles and t t pendant edges. Furthermore, the exact value of the gp {\rm{gp}} -number on wheel graphs is determined.