Pseudomonas aeruginosa colonizes the sputum of most adult cystic fibrosis patients, forming difficult-to-eradicate biofilms in which bacteria are protected in their self-produced extracellular polymeric substance (EPS) matrices. EPS provide 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 the viscoelasticity of biofilms has been related to antimicrobial penetration but not yet bacterial killing, this study aims to relate killing of P. aeruginosa, in its biofilm mode of growth, by three antimicrobials to biofilm viscoelasticity. P. aeruginosa biofilms were grown for 18 h in a constant-depth film fermenter, with mucin-containing artificial sputum medium (ASM+), artificial sputum medium without mucin (ASM−), or Luria-Bertani (LB) broth; this yielded 100-μm-thick biofilms that differed in their amounts of matrix environmental DNA (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-medium-grown biofilms. Slower components due to water with dissolved polysaccharides, insoluble polysaccharides, and eDNA were most important in the relaxation of ASM+-grown biofilms. ASM−-grown biofilms showed intermediate stress relaxation. P. aeruginosa in LB-medium-grown biofilms was 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. In conclusion, 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.