Received Signal Strength (RSS) based localization algorithms are sensitive to a set of non-cryptographic attacks. For example, the attacker can perform signal strength attacks by placing an absorbing or reflecting material around a wireless device to modify its RSS readings. In this work, we first formulate the all-around signal strength attacks, where similar attacks are launched towards all landmarks, and experimentally show the feasibility of launching such attacks. We then propose a general principle for designing RSS-based algorithms so that they are robust to all-around signal strength attacks. To evaluate our approach, we adapt two RSS-based localization algorithms according to our principle and experiment with real attack scenarios. All the experiments show that our design principle can be applied to achieve comparable performance with much better robustness.