This paper explores the addition of small stubs with anechoic terminations (termed herein “anechoic stubs”) as a means of damping and/or removing vibration modes from planar frame structures. Due to the difficulties associated with representing anechoic boundary conditions in more traditional analysis approaches (e.g., analytical, finite element, finite difference, and finite volume), the paper employs and further develops an exact wave-based approach, incorporating Timoshenko beams, in which ideal and non-ideal anechoic terminations are simply represented by a reflection matrix. Several numerically evaluated examples are presented documenting novel effects anechoic stubs have on the vibration modes of a two-story frame, such as eliminated, inserted, and exchanged mode shapes. Modal damping ratios are also computed as a function of the location and number of anechoic stubs, illustrating optimal locations and optimal reflection ratios as a function of mode number. Forced vibration studies are then carried out, demonstrating reduced, eliminated, and inserted resonance response.