Advancements in controlled drug delivery (CDD) technology still face major challenges in practice, including chemical issues with synthesizing biocompatible drug containers, releasing the pharmaceutical compounds at the targeted location in a controlled time rate and using an effective and safe trigger for initiating the drug release. This work aims to overcome these challenges with employing biodegradable shape memory polymer (SMP) based drug-delivery containers. Besides biological safety, biodegradability ensures that no further surgery will be needed for the removal of the containers. Focused ultrasound (FU) is used as a trigger for noninvasively stimulating SMP-based drug capsules. FU has a superior capability to localize the heating effect, thus initiating a controlled shape recovery process only in selected parts of the polymer, which affects the amount of drug released. The current research uses a mathematical multiphysics model which performs an acoustic-thermoelastic analysis, to optimize the design of SMP containers. The proposed designs exploit various parameters such as nonlinearity, absorption and diffraction effects, as well as input power and frequency of the propagating acoustic wave to attain the desired shape recovery, as required by the application or location of drug release. The acoustic-thermoelastic effects on the SMP containers are studied with the help of finiteelement methods. Multilayer simulations are performed at millimeter scale to mimic the in vivo conditions of a drug delivery container travelling inside an artery. By manipulating the design and the shape recovery rate of the SMP containers, velocity of the drug particles is controlled and directed towards a specific location.