We have used first principles simulation based on density functional theory to calculate the equation of state and elasticity of superhydrous phase B, Mg10Si3O14(OH)4. The pressure-volume results for superhydrous phase B is well represented by a third order Birch-Murnaghan formulation, with K0=161.8 (±0.2)GPa and K0'=4.4 (±0.01). The calculated full elastic tensor at 0GPa is in good agreement with Brillouin scattering results, with the compressional elastic constants: c11=329.5GPa, c22=294.9GPa, c33=306.8GPa, the shear elastic constants - c44=99.8GPa, c55=98GPa, and c66=99GPa; the off-diagonal elastic constants c12=82.5GPa, c13=84.6GPa, and c23=98.7GPa. At the depths corresponding to the mantle transition zone, the aggregate sound wave velocities for superhydrous phase B is slower compared to dry ringwoodite which is the dominant mineral phase. However, hydrous ringwoodite bulk sound velocities are comparable to that of superhydrous phase B. Majoritic garnet, the second most abundant mineral in the transition zone, has bulk sound wave velocities slower than superhydrous phase B. An assemblage consisting of hydrous ringwoodite, superhydrous phase B, and majorite garnet could account for the low velocities observed in certain subduction zone settings at depths corresponding to the base of the transition zone and upper mantle. Superhydrous phase B exhibits moderate single-crystal elastic anisotropy with AVP~3% and AVS~5% at the base of the transition zone. Single-crystal elastic anisotropy of other dense hydrous magnesium silicate phases phase such as hydrous phase D is significantly larger at these conditions and might play a major role in explaining the observed mid mantle seismic anisotropy.