Cased petroleum wells must be logged to determine the bonding and hydraulic isolation properties of the sealing material and to determine the structural integrity status. Although ultrasonic pitch-catch logging in single-casing geometries has been widely studied and is commercially available, this is not the case for logging in double-casing geometries despite its increasing importance in plug and abandonment operations. It is therefore important to investigate whether existing logging tools can be used in such geometries. Using a finite-element model of a double-casing geometry with a two-receiver pitch-catch setup, we have simulated through-tubing logging, with fluid between the two casings. We found that there appears a cascade of leaky Lamb wave packets on both casings, linked by leaked wavefronts. By varying the geometry and materials in the model, we have examined the effect on the pulse received from the second wave packet on the inner casing, sometimes known as the third interface echo. The amplitude of this pulse was found to contain information on the bonded material in the outer annulus. Much stronger amplitude variations were found with two equally thick casings than with a significant thickness difference; relative thickness differences of up to one-third were simulated. Finally, we have developed a simple mathematical model of the wave packets’ time evolution to encapsulate and validate our understanding of the wave packet cascade. This model shows a more complex time evolution in the later wave packets than the exponentially attenuated primary packet, which is currently used for single-casing logging. This indicates that tools with more than two receivers, which could measure wave packets’ amplitude at more than two points along their time evolution, would be able to draw more information from these later packets. The model was validated against simulations, finding good agreement when the underlying assumptions of the model were satisfied.