We construct triaxial dynamical models for the Milky Way nuclear star cluster using Schwarzschild ’ s orbit superposition technique . We fit the stellar kinematic maps presented in [ ] . The models are used to constrain the supermassive black hole mass M _ { \bullet } , dynamical mass-to-light ratio \Upsilon , and the intrinsic shape of the cluster . Our best-fitting model has M _ { \bullet } = ( 3.0 ^ { +1.1 } _ { -1.3 } ) \times 10 ^ { 6 } M _ { \odot } , \Upsilon = ( 0.90 ^ { +0.76 } _ { -0.08 } ) M _ { \odot } / L _ { \odot, 4.5 \mu m } , and a compression of the cluster along the line-of-sight . Our results are in agreement with the direct measurement of the supermassive black hole mass using the motion of stars on Keplerian orbits . The mass-to-light ratio is consistent with stellar population studies of other galaxies in the mid-infrared . It is possible that we underestimate M _ { \bullet } and overestimate the cluster ’ s triaxiality due to observational effects . The spatially semi-resolved kinematic data and extinction within the nuclear star cluster bias the observations to the near side of the cluster , and may appear as a compression of the nuclear star cluster along the line-of-sight . We derive a total dynamical mass for the Milky Way nuclear star cluster of M _ { \mathrm { MWNSC } } = ( 2.1 \pm 0.7 ) \times 10 ^ { 7 } M _ { \odot } within a sphere with radius r = 2 \times r _ { \textrm { eff } } = 8.4 pc . The best-fitting model is tangentially anisotropic in the central r = 0.5-2 pc of the nuclear star cluster , but close to isotropic at larger radii . Our triaxial models are able to recover complex kinematic substructures in the velocity map .