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Wiktionary
unshockable

a. Incapable of being shocked (scandalised or appalled).

WordNet
unshockable

adj. incapable of being shocked; "he was warmhearted, sensible and unshockable" [syn: broad-minded] [ant: shockable]

Usage examples of "unshockable".

A switch threw somewhere and she defaulted to Superintendent Frankland, the unshockable copper, the persona that could cope with this.

After six years in Fleet 397 Street, Janey was virtually unshockable and during dinner on the Friday she arrived, kept both Rupert and Billy in stitches, providing wildly inaccurate low-down on the sex lives of leading public figures.