An open-source data-analysis framework 2DMAT has been developed for experimental measurements of two-dimensional material structures. 2DMAT offers five analysis methods: (i) Nelder-Mead optimization, (ii) grid search, (iii) Bayesian optimization, (iv) replica exchange Monte Carlo method, and (v) population-annealing Monte Carlo method. Methods (ii) through (v) are implemented by parallel computation, which is efficient not only for personal computers but also for supercomputers. The current version of 2DMAT is applicable to total-reflection high-energy positron diffraction (TRHEPD), surface X-ray diffraction (SXRD), and low-energy electron diffraction (LEED) experiments by installing corresponding forward problem solvers that generate diffraction intensity data from a given dataset of the atomic positions. The analysis methods are general and can be applied also to other experiments and problems. Program summary: Program Title: 2DMAT CPC Library link to program files: https://doi.org/10.17632/c2t3vzbx9f.1 Developer's repository link: https://www.pasums.issp.u-tokyo.ac.jp/2dmat/ Code Ocean capsule: https://codeocean.com/capsule/7260490 Licensing provisions: GNU General Public License v3.0 Programming language: Python 3 External routines/libraries: Numpy, Scipy, Tomli, mpy4py Nature of problem: Analysis of experimental measurement data. Solution method: Optimization, grid-based global search, Monte Carlo method.