Transformation optics (TO) can be used to investigate nontrivial spacetime structures with inhomogeneous materials. However, the extreme curvature and large refractive indices make the implementation of a wormhole challenging. By considering flexural waves on a curved plate with geometric curvature, the stringent material requirement can be relaxed, and we demonstrate a two-dimensional analog of a wormhole using homogeneous materials within a curved laboratory frame. TO is used to understand wave propagation in such a curved space. This curved elastic space approach allows us to investigate not only geodesics but also wave redirection, tunneling, and virtual caustics of the wormhole, and will be useful to develop curvature-driven wave front shaping in general.