This paper introduces a novel method for evaluating nonstabilizerness, a key resource for achieving quantum advantage in quantum computing, using matrix product states (MPS) in the Pauli basis. Nonstabilizerness, also known as "magic," quantifies how far a quantum state is from being a stabilizer state. The proposed framework allows efficient computation of various nonstabilizerness measures, including stabilizer Rényi entropies, stabilizer nullity, and Bell magic, and enables the identification of the stabilizer group of an MPS. The method represents the Pauli spectrum of a state as an MPS, enabling the efficient calculation of nonstabilizerness measures through tensor network contractions. This approach is particularly effective for large systems, where traditional methods are computationally infeasible. The framework is demonstrated on ground states of Ising and XXZ spin chains, as well as in quantum circuits implemented in Rydberg atom arrays, where it provides benchmarks for future experiments. The paper also shows how the MPS representation in the Pauli basis can be used to compute the stabilizer nullity, a monotone measure of nonstabilizerness, and to identify the stabilizer group of a state. This is achieved by iteratively applying a diagonal MPO to the Pauli vector of the state, allowing for efficient computation and convergence analysis. The method is benchmarked on various systems, including the quantum Ising chain, where it successfully captures critical behavior and demonstrates the role of nonstabilizerness in identifying quantum phase transitions. The approach is also applied to compute Bell magic in a scrambling circuit, showing its effectiveness in capturing nonstabilizerness in quantum circuits. The framework is generalizable to mixed states and qudit systems, and can be used to improve approaches based on perfect Pauli sampling. It offers significant computational advantages over traditional methods, particularly for large systems, and enables the efficient simulation of quantum circuits and the study of nonstabilizerness in many-body systems. The results demonstrate the potential of the method for advancing the understanding of nonstabilizerness in quantum computing and its applications in quantum simulation and quantum error correction.This paper introduces a novel method for evaluating nonstabilizerness, a key resource for achieving quantum advantage in quantum computing, using matrix product states (MPS) in the Pauli basis. Nonstabilizerness, also known as "magic," quantifies how far a quantum state is from being a stabilizer state. The proposed framework allows efficient computation of various nonstabilizerness measures, including stabilizer Rényi entropies, stabilizer nullity, and Bell magic, and enables the identification of the stabilizer group of an MPS. The method represents the Pauli spectrum of a state as an MPS, enabling the efficient calculation of nonstabilizerness measures through tensor network contractions. This approach is particularly effective for large systems, where traditional methods are computationally infeasible. The framework is demonstrated on ground states of Ising and XXZ spin chains, as well as in quantum circuits implemented in Rydberg atom arrays, where it provides benchmarks for future experiments. The paper also shows how the MPS representation in the Pauli basis can be used to compute the stabilizer nullity, a monotone measure of nonstabilizerness, and to identify the stabilizer group of a state. This is achieved by iteratively applying a diagonal MPO to the Pauli vector of the state, allowing for efficient computation and convergence analysis. The method is benchmarked on various systems, including the quantum Ising chain, where it successfully captures critical behavior and demonstrates the role of nonstabilizerness in identifying quantum phase transitions. The approach is also applied to compute Bell magic in a scrambling circuit, showing its effectiveness in capturing nonstabilizerness in quantum circuits. The framework is generalizable to mixed states and qudit systems, and can be used to improve approaches based on perfect Pauli sampling. It offers significant computational advantages over traditional methods, particularly for large systems, and enables the efficient simulation of quantum circuits and the study of nonstabilizerness in many-body systems. The results demonstrate the potential of the method for advancing the understanding of nonstabilizerness in quantum computing and its applications in quantum simulation and quantum error correction.