Ultrasonic testing (UT) is used to detect internal flaws in materials and to characterize material properties. In many applications, computational simulations are an important part of the inspection-design and analysis processes. Having fast surrogate models for UT simulations is key for enabling efficient inverse analysis and model-assisted probability of detection (MAPOD). In many cases, it is impractical to perform the aforementioned tasks in a timely manner using current simulation models directly. Fast surrogate models can make these processes computationally tractable. This paper presents investigations of using surrogate modeling techniques to create fast approximate models of UT simulator responses. In particular, we propose to integrate data-driven methods (here, kriging interpolation with variable-fidelity models to construct an accurate and fast surrogate model. These techniques are investigated using test cases involving UT simulations of solid components immersed in a water bath during the inspection process. We will apply the full ultrasonic solver and the surrogate model to the detection and characterization of the flaw. The methods will be compared in terms of quality of the responses.