Thinking of literature terms I'm not sure that this question is a correct one. It's hard to imagine any 'modernist' elements in A.Pope's poetry.

The 2nd thought : Eliot's poems are definitely close in its ironic and very inter-textual style to what we call 'post-modernism'. their form is 'very opened', classically elaborated fragments with any allusions (on account of Dante and Shakespeare and so on) look non-solid, spontsneous. There is a seal of pure lyricism on these great texts. On the opposite side there is the very 'close' composition of The Rape of the Lock, that was 'predicted' by the whole mock-epic European tradition from the time of Batrachomyomachia to the Renaissance poems such as Teofilo Folengo's 'Baldus', Alessandro Tassoni's 'La Secchia Rapita', Nicolas Boileau'-Despréaux' 'Le Lutrin' , etc.

Thus, the ironical language of Alexander Pope's burlesque poems is a very traditional thing for its own genre. And Elliot's irony is really a 'modernist' and inventive thing, It easily crosses the borders of traditional genres to create something VERY new. The thing that makes incorrect any comparisons to the address of authors of previous centuries.

I do also agree with Vadim, I don't see any relation between Pope's poems and Eliot's since they both adopt different literary styles and visions. The only base on which you can post your question is the question of satire and irony, which are explicit in Pope and fragmented and stated implicitly in Eliot. 

One relation is the satiric tendencies. Both mock their contemporary societies, and both mock London, a city/civilization they perceive to be in decline.  Both have "High Church" links--Pope is a Catholic, Eliot an Anglican who later also declared himself a Royalist and a Conservative. Both give us images of a city being overwhelmed--by a scourge of dunces, in the first case, and by masses, industrialism, and alienation, in the second. You could start with Ronald Paulson's book on satire and subsequent theories of satire. 

Dear Dr Ostrom,

I am thrilled to have your invaluble critical comment concerning the satiric link in the poems of Pope and Eliot. I have gone through some of the relevant literatures and perceived the message as indicated by you.

Currently, I am guided by Alan Wilde's Horizons of Assent: Modernism, Postmodernism, and the Ironic Imagination. Do you think it is an appropirate book to begin with?

I will remain grateful to for prescribing me Ronald Pulson's book on satire and subsequent theories. I  anticipate suggestion and guideline from you in the days to come  and regard myself lucky to be in touch with such a scholarly person in life.I will  search for  Ronald Pulson's book in Nepalese market.

Sincerely yours,

Shovit Khadka

PhD Scholar, Mewar University, India