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The interaction of the twinnedβ _-1-γ ₁ ^′ , martensitic interface with various experimentally observed obstacle particles is analyzed using a specific dislocation model for the interface. The strain interaction of particles with simple shears and tetragonal distortions and their modulus interactions are treated as functions of particle crystallographic orientation, particle position with respect to interfacial intersection, and particle size. Differences from previous predictions of a simple general interface model arise primarily from differences in the assumed interfacial trajectory relative to the particles. The finite-particle calculations indicate that the point-particle approximation is valid for a particle radius less than one-tenth the interfacial twin period. Overall agreement with the experimentally measured interfacial mobility behavior is greatly improved over the …