Let $T^*_r(p)$ be the class of multivalent meromorphic functions $f(z)$ in a punctured disk $\c U^*_r$ with a simple pole of order $p$ at the center of disk is defined. We considered the class of starlike multivalent meromorphic and convex multivalent meromorphic functions $S^*_\alpha(p),C^*_\alpha(p)$, respectively. The coefficient properties are obtained and the starlikeness and convexity of functions in $T^*_r(p)$ are also investigated with some other results.