Pseudomonas aeruginosa colonizes the sputum of most adult cystic fibrosis patients, forming hard to eradicate biofilms, in which bacteria are protected in their self-produced EPS-matrix. EPS provides biofilms with viscoelastic properties, causing time-dependent relaxation after stress-induced deformation, according to multiple characteristic time-constants. These time-constants reflect different biofilm (matrix) components. Since viscoelasticity of biofilms has been related with antimicrobial penetration, but not yet with bacterial killing, this study aims to relate killing of P. aeruginosa in its biofilm-mode of growth by three antimicrobials with biofilm viscoelasticity. P. aeruginosa biofilms were grown for 18 h in a constant depth film fermenter, either with mucin-containing artificial sputum medium (ASM+), artificial sputum medium without mucin (ASM-), or Luria-Bertani broth (LB). This yielded 100 μm thick biofilms, that differed in their amounts of matrix eDNA and polysaccharides. Low-load-compression-testing followed by three-element Maxwell analyses, showed that the fastest relaxation component, associated with unbound water, was most important in LB-grown biofilms. Slower components due to water with dissolved polysaccharides, insoluble polysaccharides and eDNA, were most important in relaxation of ASM+-grown biofilms. ASM--grown biofilms showed intermediate stress relaxation. P. aeruginosa in LB-grown biofilms were killed most by exposure to tobramycin, colistin or an antimicrobial peptide, while ASM+ provided the most protective matrix with less water and most insoluble polysaccharides and eDNA. Concluding, stress relaxation of P. aeruginosa biofilms grown in different media revealed differences in matrix composition that, within the constraints of the antimicrobials and growth media applied, correlated with the matrix protection offered against different antimicrobials.