Surface acoustic waves (SAWs) provide a versatile platform for signal processing, sensing, and emerging quantum technologies, yet their functionality is often constrained by diffraction-induced spreading. Here we introduce perfect self-similar beams (PSSBs) into acoustics and develop a theoretical and numerical framework adapted for SAWs on $\mathrm{LiNb}{\mathrm{O}}_3$. Starting from the paraxial wave equation, we derive a closed-form error-function solution for an odd-symmetric 0/π entrance and design a dislocated interdigital transducer layout to encode the required phase distribution. To bridge the gap between ideal continuous apodization and practical implementation, we further introduce a multilevel voltage driving scheme to approximate the target transverse amplitude profile with high fidelity. Three-dimensional full-wave simulations confirm the hallmark properties of SAW PSSBs, including nondiffracting propagation, self-similar scaling, a robust central null, and self-healing after partial obstruction. This work establishes both a theoretical framework and a practical strategy for shaping diffraction-resilient SAW beams, with potential applications in micro/nano manipulation, phononic information processing, and acousto-optic or quantum coupling.

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• Acoustic wave phenomena
• Metamaterials
• Non-diffracting waves
• Acoustic metamaterials
• Transducers
• Acoustic techniques
• Self-similarity
• Surface acoustic wave