X-ray-induced acoustic (XA) computerized tomography (XACT) is an evolving imaging technique that aims to reconstruct the X-ray energy deposition from XA measurements. Main challenges in XACT are the poor signal-to-noise ratio and limited field-of-view, which cause artifacts in the images. We demonstrate the efficacy of model-based (MB) algorithms for 3-D XACT and compare with the traditional algorithms. The MB algorithms are based on the matrix free approach for regularized-least-squares minimization corresponding to XACT. The matrix-free-LSQR (MF-LSQR) and the noniterative model-backprojection (MBP) reconstructions were evaluated and compared with universal backprojection (UBP), time-reversal (TR), and fast-Fourier transform (FFT)-based reconstructions for numerical and experimental XACT datasets. The results demonstrate the capability of the MF-LSQR algorithm to reduce noisy artifacts thus yielding better reconstructions. MBP and MF-LSQR algorithms perform particularly well with the experimental XACT dataset, where noise in signals significantly affects the reconstruction of the target in UBP and FFT-based reconstructions. The TR reconstruction for experimental XACT is comparable to MF-LSQR, but takes thrice as much time and filters the frequency components greater than maximum frequency supported by the grid, resulting loss of resolution. The MB algorithms are able to overcome the challenges in XACT and hence are vital for the clinical translation of XACT.