What do critics think about "Jude the Obscure"? How can you criticize the story in the new classical method or Russian way?
I'll give you a sampling of some of the criticism of this novel. The introduction to the eNotes study guide mentions that when the novel was first published it received negative reviews. The theme of an unmarried couple's living together was morally unacceptable at that time.
A New York Times book review from 1896 calls the book "Hardy's Audacious Novel" and wonders whether the book should ever have been written. The writer of the article cites American critic W. D. Howells as praising the book, despite its dealing with subjects "not hitherto touched in Anglo-Saxon fiction." However, another critic as "gasping...in the outspoken fervor of her denunciation."
“There may be books more disgusting,” she says of “Jude,” “more impious as regards human nature, more foul in detail, in those dark corners where the amateurs of filth find garbage to their taste; but not, we repeat, from any master’s hand.”
The same article cites another critic, Edmund Grosse, as laying aside the social mores and dealing with the novel on its literary merits:
he finds “Jude” “an irresistible book: it is one of those novels into which we descend and are carried on by a steady impetus to the close, when we return, dazzled, to the light of common day.
I've pasted a link to that review in the Sources section so that you can read the entire article, which is very interesting. See the other links for additional information.