In this talk, we present the Multiscale Hybrid (MH) method, a new approach in multiscale finite element methods aimed at solving elliptic problems with multiscale coefficients (see [2]). The MH method is based on the framework of the Multiscale Hybrid Mixed (MHM, see [1] and [3]) method but introduces a modified Lagrange multiplier that fundamentally changes the structure of the problem. This modification allows both the local basis function computations and the global problem to remain elliptic, eliminating the mixed formulation constraints encountered in previous approaches. Using a hybrid formulation and a static condensation process at the discrete level, we reduce the final global system to involve only the Lagrange multipliers, optimizing both computational efficiency and memory usage. Through numerical experiments, we compare the MH method’s performance, accuracy, and memory demands with those of the MHM method, demonstrating its advantages for efficiently handling multiscale problems. This talk will cover the theoretical foundation of the MH method, its computational benefits, and its potential applications in advancing multiscale finite element analysis. [1] R. Araya, C. Harder, D. Paredes, F. Valentin. Multiscale Hybrid-Mixed Method. SIAM Journal on Numerical Analysis, Vol. 51, No. 6, pp. 3505-3531, 2013. doi:10.1137/120888223. [2] G. R. Barrenechea, A. T. A. Gomes, D. Paredes. A Multiscale Hybrid Method. SIAM Journal on Scientific Computing, Vol. 46, No. 3, pp. A1628-A1657, 2024. doi:10.1137/22M1542556. [3] G. R. Barrenechea, F. Jaillet, D. Paredes, F. Valentin. The multiscale hybrid mixed method in general polygonal meshes. Numerische Mathematik, Vol. 145, No. 1, pp. 197-237, 2020. doi:10.1007/s00211-020-01103-5.