A rotating/stratified fluid supports waves that propagate in directions that depend on their frequency. If the fluid is uniformly rotating around an axis Oz with a rotation rate Ω and/or uniformly stratified along the same axis with a Br¨unt-V¨aiss¨al¨a frequency N, harmonic waves of frequency ω propagate along characteristic lines that make an angle θ with respect to the horizontal plane Oxy with θ satisfying the relation ω^2 = 4Ω^2 cos^2 θ + N^2 sin^2 θ. Any infinitesimal oscillation of the boundary is a source of waves but when this boundary is tangent to a direction of propagation of the waves, a singularity generically appears. This critical slope singularity propagates along the criticalray tangent to the boundary. When weak viscous effects are considered, this singular ray forms a concentrated self-similar wave beam with an amplitude that depends on the nature of the singularity and a width of order (νxk/ω) 1/3, where ν is the kinematic viscosity and xk the distance to the critical point. The goal of the present work is to provide information on the type of singularities that can be generated in an infinite domain, and therefore on the amplitude and nature of the concentrated wave beams that can be created from critical points. We analyse in a 2D framework two generic configurations corresponding to oscillations normal and tangent to the boundary, respectively. In the first case (oscillations normal to the boundary), we obtain an amplitude scaling in (ωτ^3c /(νxll))^1/6 corresponding to an inviscid singularity in x⊥^−1/2 , where x⊥ is the distance to the critical ray and rc the curvature radius at the critical point. In the second case (oscillations tangent to the boundary), a weaker beam in (νr^3c /(ωx^5ll))^1/12 is obtained corresponding to a stronger singularity in x⊥^−5/4. In that case, the beam is generated by the peculiar viscous boundary layer flow obtained close to the critical point and the problem can be completely solved by a local analysis. A general expression for the beam amplitude is derived that depends on the fluid characteristics (Ω, N), the wave frequency ω, the velocity amplitude of imposed tangential oscillations and the local curvature radius at the critical point. Finally, the first order viscous correction to the critical slope beam induced by the no-slip boundary condition on the surface is also calculated.