Results are presented for the masses mH and mW of isoscalar and isovector states in the lattice SU(2) Higgs model with scalar field in the fundamental representation. The Monte Carlo study is done on a lattice of size 83 × 16 in the vicinity of three points of the Higgs-phase-transition sheet. The masses show only weak dependence on the quartic self-coupling λ and on the gauge coupling β, but an interesting dependence on the hopping parameter κ. At the phase transition mH has a sharp dip consistent with critical behaviour, whereas mW stays above 12a. The mass ratio mhmw becomes larger than one in the Higgs region shortly above the phase transition.