An attack-resistant network is a purpose-built network to survive attacks; by construction, it should be both resilient and secure. Resiliency is the ability to provide alternative communication paths should one path become disrupted due to failures or attacks; while security is the ability to contain and limit the impact of compromises. Interestingly, these two can present conflicting demands. In this paper, we provide a first formulation of a new class of problems focusing on the engineering of attack-resistant networks. Our model considers both resiliency and security, and uses a notion of blocking probability as a rigorous measure for evaluating different network constructions. We propose several efficient approximation algorithms for computing blocking probability and provide bounds for their errors. Based on these algorithms, we introduce a family of heuristics to guide the construction of optimal attack-resistant networks with minimum blocking probabilities. We also present extensive results to evaluate and demonstrate the near-optimal performance of our heuristics and approximation algorithms.