Jobs recently published an open letter on Apple's website criticising Flash for causing Apple products to crash and drain their batteries.
Adobe has struck back with full-page ads in newspapers including the Financial Times as well as on various technology sites.
The tongue-in-cheek ads read: "We [love] Apple...what we don't love is anybody taking away your freedom to choose what you create, how you create it and what you experience on the web."
They invite people to visit the Adobe website where co-founders and chairmen Chuck Geschke and John Warnock have published their response to Jobs, entitled 'Our thoughts on open markets'.
They criticise Apple's approach saying it could "undermine this next chapter of the web - the chapter in which mobile devices outnumber computers, any individual can be a publisher, and content is accessed anywhere and at any time."
Flash is the most widespread video player technology on the web, used by millions of sites for videos and games.