Please post an image or two. If you aren't able to do so, perhaps a friend, neighbor or relative could help you.

Here's a photo of the anomoly. Have had some much worse than this one. (i.e. more white marbling.)

Hi, m.hat--I'm a rank newbie to tomato growing, but seeing as no one else (ie, more knowledgeable) has posted a follow-up, I thought I'd suggest yellow shoulder as a possible culprit? It's especially likely in beefsteak varieties. My Better Boys clearly show signs of yellow shoulder on the skin, but if you're growing a uniform-ripening cultivar, the tomato may look perfect on the outside and still have the white tissue inside.

Try searching on the term for more info on causes and solutions. Growers seem to suggest that the blame lies with excessive exposure to direct sunlight, high temps >90F, or both--and these have certainly been factors where my BBs are growing--but the plantology pros seem to feel that the cause is more complex than that.

Soil composition is likely to be a factor, at any rate. My beefsteaks loved the spot where I planted them, so if I grow them again next year, I'll try soil analysis and nutrient correction and see what that does.

I heartily agree that the white tissue is a downer, but since the Better Boys are all I've got, and since they've been so sweet and delicious, I just excise the bad spots and eat the rest!