Well, Greek nouns' stress sometimes does "descend". There is no specific rule for all cases, but that doesn't always happen. In other words, you might come across some nouns that keep their stress both in nominative and genitive ( usually two syllable words, for exp το μήλο-τα μήλα (nom), του μήλου-των μήλων (gen), or o λύκος-του λύκου (nom), του λύκου-των λύκων (gen)).
Also, you might come across some nouns that keep their stress in nominative, but then it "descends" in genitive (for exp το αυτοκίνητο-τα αυτοκίνητα(nom), του αυτοκινήτου-των αυτοκινήτων (gen)).
I did some research for when and why stresses do descend (as a native, I'm pretty confident that they didn't teach us something like that in school, or I just can't remember it), and I found some articles like this one http://www2.media.uoa.gr/language/grammar/details.php?id=22 in Greek, explaining that it does have to do something with ancient greek.
So, the so called rules:
-Proparoxytone (with a stressed antepenultimate) masculine and feminine nouns ending in -ος and of scholarly origin, have their stress descending in penultimate in sing. genitive and in plur. genitive and accusative:
exp. ο έμπορος, του εμπόρου, των εμπόρων, τους εμπόρους
η είσοδος, της εισόδου, των εισόδων, τις εισόδους
-Proparoxytone neuter nouns ending in -o and of scholarly origin, have their stress descending in penultimate in sing. genitive and plur. genitive:
exp. το σύμφωνο, του συμφώνου, των συμφώνων
(exception to these rules above are the nouns with more than 3 syllables and the nouns of demotic, *folk origin, and most family names, that keep their stress.
exp. του αντίλαλου, του λυκόσκυλου, του κάρβουνου, του Αργυρόκαστρου, του Θόδωρου, του Χριστόφορου, του Χατζόπουλου, του Ξενόπουλου etc.)
-Neuter nouns ending in -ος have their stress descending in ultimate in plur. genitive.
exp. νέφος - νεφών, στέλεχος - στελεχών
If any of those are proparoxytones, they have their stress descending in penultimate in sing. genitive and in plur. nominative and accusative.
etc. το στέλεχος, του στελέχους, τα στελέχη
NOTE: Adjectives' stress DOES NOT descend. . There are a couple more rules, but they have to do with ancient Greek, and my opinion is to not bother yourself with that just yet, since all of the above are a bit complicated by themselves.. Stresses eventually become a matter of "habit".
I hope I helped you a bit ^.^
Neuter nouns in -ι also have the stress on the final syllable in the genitive (singular and plural): το σπίτι, του σπιτιού, των σπιτιών.
And nouns in stressed -ί also have the stress right at the end not only in the genitive (singular and plural), but also in the nominative plural: το παιδί, τα παιδιά, του παιδιού, των παιδιών.
And old first-declension feminine nouns have the genitive plural ending stressed: η κυρία, των κυριών. Now that third-declension nouns got merged into first-declension ones it's hard to see which ones this applies to :) For example, η κοινότητα becomes των κοινοτήτων (only one syllable further down) not των κοινοτητών (on the final syllable) since it's from old η κοινότης (third declension, not first).
A very odd stress movement backwards occur in some local names which are given in neuter pl (also that is odd)
τα Χανιά, των Χανίων, τα Σφακιά, των Σφακίων
Not always though: τα Κύθηρα, των Κυθήρων moves the stress "normally" ie. forward
1.Why are the names of these places in plural?
2Why does the stress move backwards in gen. pl?
Some feminine nouns ending in -η form plural in -εις. Η άσκηση, οι ασκήσεις, η πάθηση, οι παθήσεις, η λέξη, οι λέξεις, η πόλη, οι πόλεις.
Those nouns come from ancient Greek nouns ending in -ις (η πόλις, η άσκησις, η πάθησις, η λέξις) and also have an alternative, more formal genitive in -εως (λέξεως, πόλεως, ασκήσεως, παθήσεως) and also form genitive plural in -εων instead of just -ων (ασκήσεων, πόλεων, λέξεων, παθήσεων).
A native Greek automatically knows how to decline each noun, but a learner must take note and learn by heart which feminine noun in -η forms plural in -εις or -ες. :)